If you’re a single parent with one young child, you can’t self isolate away from them, but you’d both isolate in your house.
If you have more than one child, you’d still all have to stay in your house, but you’d try and isolate sick child from well child. If it’s you who has got it, you’d have to just try and have minimum contact with your children. But probably assume they will catch it from you.
If there are two parents, I think one of you would have to sacrifice yourself to stay in the room with infected child. Obviously if parent is infected the other parent looks after the children.
I doubt you’d get anyone to look after your children if you were infected as your children are likely to be too and you’d be spreading the infection to the babysitters.
With dogs though, maybe someone else would be willing to look after your dog for you? Although there might be a chance that dogs can carry the virus (not sure if the dog as a virus carrier has been debunked or not?). I think if you didn’t have a garden, you’d just have to “exercise” your dog by throwing balls or whatever in the house/flat.
As for going stir crazy- you’d just need to put up with it. Nobody thinks self isolation is fun, it’s just something you have to get through.
Although, if I got to spend two weeks in my room away from the children with plenty of food, tv, books and some craft or jigsaws... hmmm it does sound fairly pleasant rest!!