Can the people telling the OP to just take the dogs and rehome them behind their owners back, sit down, shut up and give their heads a wobble?
Thats theft.
It also puts any rescue centre DEEP in the shit when the owner finds out whats happened.
It could also impact on anyone taking on those dogs from the rescue should things get that far before the owner finds out whats happened.
Yes, the OP should have said something far sooner and yes, were this a neglect case in court she'd be potentially seen as aiding and abetting or guilty of neglect herself because she has inadvertently allowed herself to be the adult in charge of these dogs at times.. Unfortunately 'they aren't my dogs' is not a defence for ignoring welfare issues in animals you share a home with.
Advising stealing the dogs however is further compounding the issues in an already horrible situation.
OP you must speak to their owner and tell her the neglect stops now or you will take action.
She is failing to meet several requirements under the Animal Welfare act, including causing suffering by failing to give medication, causing the animals to live in filthy conditions, not meeting their physical or mental needs...
In your shoes, I would either - take over the dogs care myself, and ensure I get bills for medication, vets, dog walkers, daycare, food etc - and then use that evidence to prove she's abandoned the animals (and then you would potentially be in a position to rehome)..
Or, leave, do a flit and leave her to pay the outstanding rent.
I think when you put your foot down, she's going to get rid of the dogs, or disappear, either way leaving you to pay for the damage her dogs have done to the property or even leaving you with the dogs as well. I do not see a way out of this that isn't going to cost you unfortunately.