I had experiences with a family that said things that initially appeased my concerns in the interview, only to find out later that what they said was the truth stretched quite far. After having both their children for 4 months, I gave them their notice last week & the next day they pulled them out. If parents aren’t willing to work with you (& by “work with you” I mean not lying & willing to work together), then I would definitely terminate. I put off terminating this family for months because I loved both of their children, but I just couldn’t do it anymore.
Do it for your sanity, for the other children in your care (if there are any), & for his as well.