Try Feliway plug ins.
Keep her in one room, she might be stressed.
However, I adopted a cat that would wee anywhere, never found any definitive medical reason, possibly nerve damage from an accident but also possible behaviour issues from early life. Spent a fortune on Simple Solution, vinegar and kitchen roll over the years.
Your poor cat sounds traumatised, hence my suggestions above. Vet procedure is test for UTI and give Metacam, antibiotics.
I would suggest feeding wet food only as dry can cause discomfort in the bowel/constipation which then irritates the bladder.
Could you give her a room of her own with a washable floor and keep her in it? A radio playing quietly, Feliway plug in, sit with her and cuddle her, a covered bed or cardboard box on it's side to hide in - all the things that are recommended with a new, shy or nervous cat, even if she didn't appear to be nervous.
Peeing inappropriately is a sign of stress, trying to tell you something is wrong, or just never been litter trained. She might just need time. may not feel happy around small children?
Have been there, it is tough but give her a chance to settle, slowly. Be prepared that it may improve but also may not be perfect, she needs a lot of love and understanding, if you are stressed by it she will know.