Being a step mom with a difficult ex girlfriend

Sadie

So my husbands ex and him have a 2 year old. We have standard visitation which is every other weekend, odd year holidays and so forth. We hardly ever got to see his daughter because her mom would refuse visitation because she absolutely dislikes me. However recently, she cheated on her new husband and he kicked her out, she doesn't have a car because it was in his name and he turned off her phone, she doesn't work and is staying with random friends. Because she has no where to go she has been asking me to keep my step daughter every weekend. Even though my husband works out of town and it's just me and our son. She hates me so much she even filed a false CPS case on me before when I had my newborn and now that she's in a bind she just practically wants me to raise her daughter! I have her Friday- Monday. It makes me angry in a way because she's done so much to effect our lives and now because she has no one else she's relying on me. Of course I never say no because I love my step daughter and I don't want her sleeping on strangers couches but do you guys think its right for me to contact CPS about the situation? Especially since the last couple times my step daughter has been here she has strep throats and her mother won't take her to the doctor and I can't because she won't get insurance on her. I don't want to make her mad and keep her from us but the situation she is in is not suitable for a child. And if she's going to be staying with us so much I feel like maybe we should be the custodial parents and provide her mother with standard visitation? Anyone have anything similar?