I am sorry for the loss of your father. I'm your mom's age and yes, thanks to your father's service time, she is set for life.
1. Consider holding off on making any changes that do not need to be made right now.
You are grieving and it is hard to be level headed during such a trying time.
2. I assume it will take a while to find a buyer for the farm, this will give your mom a bit of time to say good-bye to the place, (and give her something to do) time to pack up and/or let go of her memories and treasures.
Just because she is willing to sell the place and knows she couldn't deal with it on her own doesn't make it any easier leaving behind her life as she knew it.
3. Children have good intentions but as long as she is of sound mind and body, she should have the final say in how and where she lives. She may change her mind in a year - why not? Once she's out of mourning and has made the rounds with the kids, she may decide a nice little condo of her own would suit her better.
Privacy and having control over your own life is freedom, she already has security - all you need to do is be there for her when she needs you or make new, different arrangements when the time comes and she can't live on her own.
My family is long-lived - so I decided it was OK to spend $5K on improvements in the garden because I'll still have a minimum of 10 years to enjoy it. By 80-90 I'll just sit out there with a cup of coffee in my hand enjoying the butterflies or watching the birds and the squirrels. It will probably do me good to putter about a bit, but I already planned for low maintenance and a nice little gazebo area where I can just tend a couple of flowerpots instead of a vast garden.
... and in the event that I do die earlier, I will have enjoyed the pleasure of one more project that made me happy.
Do take the time and really listen and consider your mom's wishes. Have several conversations with her over the next year and let her know she can always change her mind. She may be happy to have you handle her monetary affairs and be too overwhelmed to make any decisions on her own at present, but at 70 she will have definite ideas on how she wants to continue living her life.
Living three months with each of her children may be fine for right now but down the line, she may feel differently or choose to live on her own, with a friend in a retirement community or permanently with one of her children.
4. The sister who is already planning on a larger car and house may be a problem. If she is someone who truly cares for your mom despite her spendy ways and immediate tendency to try to take advantage of the situation - well then, if she is close to your Mom and Mom would be happy there, it could be a future solution, but would require your financial (strict) supervision).
However, this could just as easily spiral out of control and turn into elder abuse by a greedy tyrant who is only looking out for herself. Mom is probably unlikely to die in five years and just that statement or perhaps expectation alone is truly worrying.
If she lived there with her with no one else to see what really goes on then it is entirely possible that your mom may give in to pressure mainly because she is currently at her most vulnerable and in a more fragile state of mind.
If you think there is a possibility that your mom may need to be shielded and protected I'd strike this sister off the rotation list, period.
5. You didn't mention whether your mom is financially savvy or not, can she handle her own expenditures, bills and so forth?
It would help if you set a monthly/annual budget together with her to have available to draw from each month. It will give her a better idea of what she has and how much she can comfortably spend each month - whether she actually spends it or not is not the issue. She needs to know she is secure, no matter what.
Besides that establish a separate account for vacation, extras - frivolous things and emergencies. She needs to know she can safely draw on X and enjoy her life without any money worries.
Even frugal people spend money and it is entirely possible that there is a thing or two she'd like to do that she hasn't ever done or not done in a long time, because she was busy with your dad or he didn't have an interest in it.
Could be anything from seeing a long lost cousin your Dad didn't care for or buying something crazy or just seeing a broadway show or an expensive exhibit - just sayin'.
Her life is not over, just very painful right now.
Give her a bit of time to rediscover herself and deal with the grief of losing her husband and her home.
6. Eventually, she will have different expenditures and expectations in her new life - so this is not the time to set budgets in stone or force decisions that might not be ideal in a year from now.
You may have to be on the alert about sis wanting money for a new expensive lifestyle that she could never afford on her own.
Keep the lines of communication open.
7. Ditto on the power of attorney and everything else you need to set up ahead of time so if something happens you can step in and make decisions - solo.
Your dad had enough confidence in you to entrust your mom's finances to you, better yet, so does she.
Honor it by keeping her best interests at heart, letting her make her own decisions and protecting her from anyone who thinks mom's money is a free for all or a license to live well above one's means.
I will not address the investments since I have no experience, but I happened across this post this morning which discussed a strategy you may find helpful in your decision-making process.
The discussion as such includes considerations and a pragmatic approach to what course of action to take.
https://forum.mrmoneymustache.com/ask-a-mustachian/92-year-old-investor-recommendations-needed/I think that Laura 33's answer would be helpful in arriving at and handling annual expenses/budget in a simple way so that your mom always knows what annual funds she has available.
Again, my condolences and my best wishes for the future.