Yup. Been there, have many teeshirts.
Both my mother and my inlaws were pretty crazy for years. Resulted in a total cutoff of inlaws. Husband still has no contact with his mother other than sending her a birthday card... used to send mother's day cards, but he stopped that after she sent one back with a rant written all over it about how
she has no idea what she did and she just cries and cries all day every day... She knows what the conditions are, she just refuses to acknowledge the boundaries and is angry about the fact that her son is an adult and won't let her run his life anymore.
So first things first:
You need to work on YOUR feelings of guilt and responsibility towards your mother. She is taking advantage of you and disrespecting you. You have two choices when this happens - allow it or don't allow it. It really is that simple. Choosing to tell someone that you have firm boundaries is not something you should feel guilty about. Enforcing said boundaries - same thing. She is the one that should be feeling embarrassed and contrite, but instead she flips it back on you (projecting her poor behavior as your fault) since she should be allowed to do whatever the hell she wants? No. Just no.
Think of your mother as a 5 year old. (okay, stop snickering) But really, this is the attitude you need to adopt. She is acting out and has no boundaries unless you place them there and give her firm consequences. If your child was being a crazy brat, would you ignore it and let her run all over being a brat? I don't think so. You'd tell her to stop, then you'd tell her what behavior you'd expect from her, and there would be punishments/corrections if she continued. This is really the same thing.
You're not asking for unreasonable things. If you weren't related, you would have already stopped trying to include her in your life. Friends and more removed family don't get to treat you like crap and run roughshod over you, so why should close family? They are supposed to love you and care about the relationship you have together. She is clearly saying that your wants and needs are not important.
Definitely start working on the idea that you are being reasonable, you are not being mean or rude or hurtful. You are asking for basic things - she's the rude, unreasonable bully here.
So what do you do about bullies? You give them very clear guidelines. You tell them in plain speaking exactly what you want and expect from them, and then you tell them the consequences of their violating those guidelines.
And you follow through. That is definitely the hard part. But it gets easier each time you do it.
For instance, about your daughter's party: Tell her "Mom, here is what I want from you: The party is at 2pm on Saturday. I expect you to show up on time and be pleasant. Any rude behavior and you will be asked to leave. If you love me and your granddaughter, I would hope this is possible, but if you feel you can't contain your dislike of other guests attending, do not come to the party. And just a word of caution; you will not be invited to future events if you do come to this event and don't behave nicely."
And the follow through is this: if she behaves herself, positive reinforcement in the form of acknowledgement "mom, I know you dislike the inlaws, but I really appreciate the fact that you were nice to everyone and "daughtername" is so happy you could be here for her birthday. Thank you."
If she shows up and starts making rude comments or otherwise being disruptive. Either bring the party to an end early, or pull her aside and remind her that she is to be on best behavior. "mom, I heard you saying 'snarky thing' to MIL. That's exactly what I was telling you is unacceptable behavior. If you can't control yourself for just a few hours for the kid's sake, please leave."
But honestly, if you know for a fact that she will show her ass at this party... don't invite her. Have the event without her. Go to visit her if your daughter wants to see her other grandmother, and tell her if she asks that no, you didn't invite her because she had proven in the past that she didn't like the inlaws and refused to act nicely around them, so rather than ruin your daughter's birthday, it was best if she didn't come. If she wails and complains, tell her that it is on her own head that she is not being invited to events. If she can promise in the future to behave more appropriately, you might be able to start including her in larger get-togethers again but that is completely up to her.
In future, be very clear about what you want (or don't want) from her. And visits should be you going to her rather than her coming to you. The reason is that you have control then on when you leave. IF she insists on berating you, or going on about something you told her you do not want to hear, then you tell her to stop discussing this or you're leaving. And LEAVE IF SHE DOESN'T. "Mom, I'm not going to talk about this stuff and I've asked you to stop but you won't so we're going to cut this visit short. I'll see you sometime next week."
Same for phone calls. If you are chatting and she starts in, one warning "mom, I told you I am not discussing this with you. Please change the subject." she continues on same subject... "okay, you are ignoring me, so I'm going to stop you there and I guess we can talk another time when you're willing to have a pleasant conversation with me." Then hang up. Really. And don't answer if she calls back. She gets a time out - we used to do one week of no contact and then call up and see if they were willing to chat about other things and check in. No "So sorry I had to hang up on you last week" or anything. Just be pleasant and if she starts in with the hurt routine "you HUNG UP ON Meeeeee!" Tell her that you told her clearly that would happen if she persisted with X behavior. Then tell her that you love her and are willing to work on things if she's willing to do the same. If she starts the wailing and crying thing again, repeat the same script.
And every time your mother cries at you... you have to recognize that this is blatant manipulation. She KNOWS that works on you because she keeps doing it. It's her ace up the sleeve. I remember one therapist saying something along the lines of "of course your mother knows how to push your buttons. She's the one that installed them!" You have to tell her that the crying is very manipulative and she is capable of talking to you without crying at you, and you expect her to do so.
If she's the drop by your house type? First, if she has spare keys, get them back and make sure to change the locks if you think she made copies. Tell her that drop bys are no longer allowed. She needs to call to make sure it is a good time, and accept no for an answer if it isn't. If she still drops by. Two things: you don't have to answer your door. If she can't see in the house, how does she even know you're home? If she can see in, answer the door, but block it with your body, and tell her now is not a good time, she was asked to call first to make sure and that you had other plans and shut the door.
ETA: one of the books recommended (I think the Emotional Blackmail book): Don't get caught up in the mistake of letting your mother manipulate you into JADE. You are allowed to say "because I said so" or other variations because you are a grown ass woman. :D
http://outofthefog.website/what-not-to-do-1/2015/12/3/jade-dont-justify-argue-defend-explainSure some of this sounds rude on the face of it, but she is sounds like my MIL; the type that will not listen to you until you are forced to be blatantly blunt and then accuse you of being mean and then using tears and tantrums to try to get you to ignore the fact that you did not actually do anything wrong. Being nice hasn't gotten you very far as it is really easy for this type to bulldoze right over you and then get angry or cry and whine with you ask them not to do that. So you need to stop asking for their permission to set up your boundaries. You need to do it and make sure to stay strong on them. So say things without anger, pleasantly, but VERY FIRMLY. If she was the type that would be able to moderate her interactions with you where you didn't have to set boundaries... well, there wouldn't be a problem at all would there? So don't get caught up in the idea that you're being rude or hurtful. Her actions have forced you to be much more firm about this than you ever wanted or should have to be. But because you care about her, you're still wanting to make an effort to include her in your life... that is you being a good person and she should be damned grateful you are still willing to do this! ;)
My own relationship with my mom has improved considerably, but it took some work (counseling too) and constant enforcing of boundaries on my end, and she honestly was able to take a giant step back and see how her behavior was hurting our relationship and make changes on her own. In my husband's case, his mother remains incapable of introspection and personal responsibility, so he holds out no hope of her changing and remains pretty much cut out of our lives (which on the surface sounds sad, but honestly it is bliss not dealing with the constant drama and anger and demands).
A few books that might be of interest (and helped both myself and my husband immensely):
http://www.amazon.com/Emotional-Blackmail-People-Obligation-Manipulate/dp/0060928972/ref=sr_1_3?s=books&ie=UTF8&qid=1460926437&sr=1-3&keywords=susan+forwardhttp://www.amazon.com/Toxic-Parents-Overcoming-Hurtful-Reclaiming/dp/0553381407/ref=pd_bxgy_14_img_2?ie=UTF8&refRID=1F6PH2CT75FC3NV986HYhttp://www.amazon.com/Stop-Walking-Eggshells-Borderline-Personality/dp/1572246901