In a couple of weeks I will have 2 teenagers in the house, as you say most of the children affected are grandchildren, like mine, although if the PWD is in the same house as grandchildren the issues can be the same.
I don't really have any answers to help you I don't think.
My mum had to live with us for a few months and it did cause issues with the children and prior to that when she babysat (whilst childminder on holiday and we were at work) I realise some of the poor judgement calls she made which I got very cross about were due to dementia.
My daughter, then aged 12, found it hard to be at home on her own with grandma during those few months she stayed as dau was at local high school (less than 10 mins walk away) she was home a few hours before we were home from work. Dau was quite mature for her age and understood why grandma was behaving as she did, but at that stage grandma expected dau to do what she was told, and this made things hard. I think if she had had friends houses to go to she would have done, but due to bullying issues she didn't (long story and ultimately she moved schools) Doesn't help you, but just hopefully shows others with same issue.
As you say children are too old for childcare, his social worker clearly hasn't got a clue.
Have you explored things like daycare, so that children can have some time in the house without 'issues' arising - particularly with upcoimng school holidays.
Most schools have someone you can talk to who helps with pastoral support, your children are likely to be coming up or in the middle of big exams int he next few years.
I understand your comments re birthdays/sleepovers - I wouldn't have felt comfy when my mum was here to have a sleepover, her comments were too blunt at that stage, ironically now she would be unlikely to comment and be rude, with the progression. She would have expected to be able to tell the other children off when she deemed appropriate - applying standards of the 30s and 40s, not even my childhood era.
Some have found a motorhome works with a PWD, maybe this could work with a family camping trip (they can be hired) and a quite beachside campsite with coastal walks might allow some way of everyone getting something out of it.