I have OCD (I don’t just like things clean and tidy, I have a diagnosis) and live my life in a similar way to you OP.
I like a strict routine so I know what to expect, I hate other people coming into my house and wouldn’t cope with the noise and mess from kids playing.
I would have desperately struggled watching the kids making paper mache because of how messy it is, it wouldn’t matter that it isn’t my house.
I would however appreciate someone doing the messy activities with my kids that I am unable to do.
I think your neighbour sounds like a lovely person and I wish I could be that laid back and carefree, I’d prefer my children to grow up like that as opposed to like me. If you struggle with tolerating mess and chaos at home then this is a good opportunity for your kids to experience more freedom and a relaxed happy environment.
I understand your routine works for you but you also have to think about what’s best for your kids, don’t you want them to look back at their childhood and have happy summer memories? You don’t get another childhood and the innocence is fleeting, there is plenty of time for early bedtimes, rules and structure in future - life is mostly like that as you get older.
What other things do you do with your kids? Will you be more relaxed in the holidays? What about weekends? If your kids don’t have play dates do they see other kids at the park or soft play? Is it just keeping your home nice that prevents your kids playing with other children?
You are the parent and in some situations you just need to say no and stick to it, if the kids continue mithering then teach them it doesn’t work. It would probably mean a lot if you said the occasional yes though, the more you relax the routine the easier it’ll get and that sense of panic will lessen.
Your kids don’t need a bath every night it’s not great for their skin, could you let them play during the time they would have a bath some nights?
This weather won’t last forever so you won’t have this issue for long, if you let your kids relax and play out you could use the time to yourself as an opportunity to do something nice for you as well.