read the first line of the first paragraph in your first post

as soon as she loses her money because you have more than her, you will have basiclay agree'd to look after the kids and support them financially as she won't be able to and won't get a place to stay if she's taken off the housing list

it is indeed a right can of worms

a mate of mines siste is a single teenage parent (well, she was back in the day) and got into all sorts of touble when the council found out that her brother was spending the nights there at her 1 bed council flat (he worked nights as recovery and used to help out looking after the baby while she had a bit of shut eye so it was all above board and stuff, he had his own house etc) so it might look to you very simple, but as soon as there is a problem then all hell can, and normally does, break loose

tell her to stay put until she's sorted a place out for herself, then look at co-habiting in her gaff

at least that way if you leave she won't be in the shit, and more importantly, the kids won't be in the shit either, and nor will you