First, don't freak yourself out. These past few months have been tough on everyone, and many fully-grown adults are doing and saying stuff that you'd never expect. It is not at all surprising that the kids are acting out, either from their own boredom/stress, or because they are reacting to additional stress in the home (my own DD was the freaking canary in the coal mine, often responding to my stress before I even realized I was feeling any!).
Second, you are legitimately angry and hurt and upset right now. So give yourself some time to deal with your current crisis and manage all of the attending emotions before you do anything. Use that time to think about what is bugging you and what your various options might be.
As you are thinking things over, I very much encourage you to try to view the situation with empathy. This child sounds like a huge handful. When most people see kids like that, they immediately assume it is the result of lax parenting -- and it's true that parenting that is either too lax or too authoritarian can aggravate the situation. But many kids are just born different. And when they act out, it is because something is wrong -- maybe they need more time running around, maybe the lights are too bright or the noises too loud, maybe they need more attention from their parents, maybe the seam on their sock is running the wrong way and irritating them with every step, maybe they're really upset about something else entirely and this is the only way they know how to express it. The parents' job is to separate the kid from the behavior -- to establish and enforce clear, consistent boundaries, while figuring out what's going on with the kid so they can figure out how to fix the underlying problem.
And let me tell you, as a parent of one of those, it is absolutely fucking exhausting. You are always "on" -- always trying to see around the corner to figure out what the next opportunity will be for the kid to go off the rails, always trying to manage things like food and sleep and outdoor playtime and quiet time and all the other things your kid needs to help her stay on an even keel, always dealing with the next developmental stage right when you finally started to figure out how to manage the last one, always trying to find diversions so that you don't spend the whole damn day saying no and fighting tantrums -- and always second-guessing yourself about every single one of those things that you didn't manage to execute perfectly. And then you get up the next morning and do it again.
And that's when the kids go to school every day and you can entertain them with movies and playdates and birthday parties.
I say all of this because if you want to approach the situation in a way that may help, you need to put yourself in the other mom's shoes first and imagine what she deals with on a daily basis. Maybe she is lazy and way too lax and lets her daughter run wild. Or maybe she was looking forward to the visit as a much-needed break and expected the kids to entertain each other so she could have an adult conversation and turn her mom brain off for a little bit, and she was totally horrified when her daughter went off the rails like that and is now beating herself up for trying to take a break and is hugely embarrassed to face you. If it's the first, then nothing you say is going to make a difference. So assuming it is the second, how would you like someone to approach you in this situation? An attitude of "your kid is a problem child and you need to man up and fix it" is going to go over very, very badly, because you are fundamentally judging her parenting without actually knowing anything about her or the kid, and she's going to feel like she has to defend herself and her kid against the attack. You're much more likely to make progress if you speak with empathy, like "Julie seems to be more impulsive than usual -- is everything ok? That must be very hard to deal with, particularly with all of the quarantine restrictions. Is there anything I can do to help? Do you have someone like a doctor or therapist who can help you deal with this?"
Same goes with the kid, btw. Kids know when adults do not like them. And from what I've seen, that tends to make them act up even more. NOT because they're trying to throw it in your face -- but because most kids want to be good and earn praise, and when they know they are not liked, they get much more anxious because they know they're failing in that, and that anxiety ramps up their stress level, and they're not mature enough yet to manage that kind of emotion, so it comes out in completely inappropriate behavior. That doesn't mean you let the kid run wild -- far from it. What it does mean is that you have clear, consistent rules, and that you implement them calmly and with love, not with anger and "I told you not to!" And if things don't feel right and it seems like tension is building, then anything you can do to provide a diversion and defuse the situation -- snack time, get out the sprinkler, everyone play tag, whatever -- is far, far more effective.
Depending how "normal" your kids are, it may help to do some reading up. I highly, highly recommend "Your Spirited Child" (saved my sanity) and "1-2-3 Magic" (whether you implement the method or not, high-strung kids really, really need the calm approach and knowing what to expect that that book lays out).
