As others have said, back to toilet training from basics.

First - get the carpet cleaned. You can hire a carpet cleaner and get pet odour solution to go in it. (Be careful with the solutions as some are poisonious IIRC - it's been a couple of years since I had mine done and I have to confess my mother sorted it for me) and use biological powder to wash your bedding. If you have duvets, these will need cleaning too (though it might be cheaper to buy new)

This will remove any scent that may be encouraging her to pee to reinforce her scent indoors.

Next - basic puppy training. Not easy with small children around but not impossible.

Take her outside (and any child that can't be put in a play pen in sight of the window unless your oldest is mature enough to watch the youngstes) everytime she wakes up, finishes play, finishes eating and at hourly intervals. With a good routine you can manage the children and toilet time.

Watch for signs - sniffing and circling are classic signs. She does this - take her out.

Praise lavishly and reward with a treat or a game when she pees outside, maybe even introduce a command word (I stupidly use 'pee-pee' - 'get busy' or 'business' is much less embarrassing)

If you catch her in the act, calmly a quietly put her outside - go out with her and praise if she finishes outside.

Any accidents you don't catch, clean up with biological wahing powder or a pet accident spray. Do not punish her - she won't understand.

Consistency is the key. Praise the good behaviour, ignore the bad.

A word on crates - they aren't cruel unless used cruelly. My dogs love their crates. It is a space that is all their own and they go there when they want some quiet time. But you need to use them right - always a positive experience. Crates are very good if you have young children - teach the children that they never go in the crate and the dog always has an escape.

That said, I'm not sure a crate would solve your problem. I understand the theory with keeping puppies dry at night - puppies will instinctively keep their bed area clean as they are vulnerable to predators in the wild. But your girl isn't a baby puppy anymore. That said, no-one likes to lie in their own effluence.

It is going to take time and some effort - especially if she has been punished for peeing indoors (she may not pee infront of you if she has learned she might get shouted at) but you can get there

Getting a cat clean.....a whole other post and whole other psychology!!

And separation anxiety....out of my experience. Perhaps a separate thread might attract advice from the more experienced.