What should i do with this lady and her daughter and my supervisor?

There is a new little girl who came into the daycare center i work at 3 weeks ago. her mother is and manipulitive. she is very demanding and my supervisosior is basically on her side. when the mother and child first came in i was on vacation prior to her comming to the place i work she was in another daycare for a week and her mother freaked out and took her out. yesterday my suprevisor was out and so i had to step in as lead teacher for the cl and i did. this lady comes into the cl room already with and attitude and starts to question us and then has a complete breakdown. today this little girls mother came in to meet with my supervisor. well the outcome of their meeting eas me and the way i interact with her and her daughter. there are 7 other childrern in this cl bu the way. my main concren with this mother is that she is not receptive to me and puts up a wall everytime no one else is in the clroom with me. but i feel like i am being put under the spot light because i don't have a fake personality like my supervisor does. the baby cries non stop when no one is holding her she is needy and clingy and most of it comes from her mother. he mother made us a care plan for her to tell us how to take care of this baby. she reallt pushed me over the edge today when she said i am cold and calous and i basically don't do my job good enopugh for her and my suprevisior who i also considered my friend at one time now sats after working there for two years that she has concrens about me. and she al;so accused me of abusing her daughter. which is not true at all i am a single moyher with two of my own happy healthly intelligent a social children i do get frustrated because the fist day this baby came in she cried for .3 hours and 40 minutes exactly. it relly hurt me to finally see tha t no one has my back and i am basically stuck and feel defenseless with this women ans my supervisor well i have nothing else to say to her at all. should i quit or should i wait it out to see the outcome.