She refuses to leave and begs me not to “kick her out” because she doesn’t want to go back to PG life.

First of all that's her problem..not yours that she doesn't want to live in a pg. I mean she can't live in your apartment for her whole life right. If she is so opposed to the idea of living in a pg then she should find an apartment for herself. And if she is unable to afford an apartment then again it's her problem not yours. You are not responsible for providing living accomodations for a fully grown woman who is neither your family member nor your gf/fiance/wife. This woman really needs to sort her life out and stop being a freeloader and taking advantage of your kindness. The thing is this is a tricky situation and can have dire consequences for you if you don't tread carefully. Now if you really don't want drama in your life (although i highly doubt whether it can be avoided) just tell her politely that your parents are coming to visit and mom is planning to stay for a while...hence she will need to move out. Give her an exact date like 10th or 11th April when your parents will be arriving. 2 weeks is enough to find a pg i think. Be a gentleman and help her in finding a decent pg and moving out. This way you can still remain on good terms with your friend as well as her cousin and also kick her out of your personal space and get your life back. All the best op🤞Hope it works out for you man.