You and the other mother are totally in different places. You are recovering (which I am so happy to hear) and you are exhausted.
That mom, for whatever reason, has decided that your home or your daughter are not for her daughter. So she either accepts and then (rudely) cancels at the last minute, or she keeps suggesting another option. I wouldn't worry about housekeeping issues on either end. I think she MAY have concerns about all the electronics (Skype, games, youtube) and it doesn't matter that her kids might be on their devices far more than your kids are. The fact is, you don't really know what goes on in her house, and she doesn't know what goes on in yours. For all you know, her daughter TOLD her that they made youtube videos and you said it was fine. Maybe her daughter is trying to get a rise out of her mom, maybe she's lobby for even more lenient rules, who knows? If the daughter is too immature to be able to go to a restaurant, or so rude that she says she doesn't like the restaurant you chose, she's not ready for this kind of intense friendship. Perhaps she's so used to her mother changing plans, challenging your plans or criticizing that she's learned it's okay to do this in social relationships. Maybe she's just a dominant personality who likes being sort of in charge of your daughter, going into her room to do stuff they all know they shouldn't do, and so on.
You can't keep begging for dates, you can't beg to get into the Scout troop, you can't keep bargaining over home/skating/park/mall.
Your daughter, meantime, like all kids, needs to learn to adjust to disappointment. She needs to learn not to put all her eggs in one basket, as if life is awful if she can't have a sleepover. She needs to branch out and have other friends who are more reliable. It's really okay to explain to her that this other family has different schedules, priorities, styles, rules and manners. Instead of always always ALWAYS being disappointed, your daughter needs to try some other things and people. You already said that she was happy about this restaurant, so go with how fun it will be, how nice the water is, blah blah. You can't always look at the glass as half empty, you know?
And, I'm sorry, I do agree that the electronics have to come out of the kids' rooms if you can't supervise. It's not enough to "try" to do better. I believe you that this other mom is a pain in the neck, and rude with the last-minute cancellations. BUT, she's right that kids should absolutely not be able to record anything at all without parents knowing what's going on, because they are too immature to know what's acceptable, they egg each other on, and the next thing you know, stuff is on the internet or texted to some of the other kids. It doesn't matter that they know your rules. It matters that they follow them. This will be a big legal/liability headache for you in the future. You might think that Minecraft is harmless, but you really don't know what they're doing in that room all the time, and it only takes a second for them to get into something they shouldn't. Until your health is fully restored, and even after, you probably should revisit your rules for other kids in your house behind closed doors.
Your daughter needs other friends. Not going to another kid's house for 2 years just isn't right. This girl is not her best friend because the get-togethers are not workable, and there are two very different parenting styles at play. Your daughter needs a larger group of friends, at least some of whom can have dates or sleepovers. Meantime, be sure to use this is a teaching moment for your daughter to discuss manners, how to behave with another's parents, how to be grateful for things you don't necessary like (restaurants, meals served, computer rules, etc.), and so on.