Parents, is this how you would treat your tutor

I work with a family where the father and mother work a lot. I was put in a groupchat with the family (the parents and the grandparents) so everyone is aware of timings for tutoring. Even then I felt like the father was making decisions without consulting his wife as I saw his wife storm out of the room when she realised she did something without talking to him. It was awkward to say the least.

It was okay for a few months but recently he has been messaging me telling me he needs help managing his son and how he needs to meet for a few hours (often with no regards to my schedule). Eventually he decided it best to just email me and we had a phone call where he said he feels I see his son more than he does. He wants me to manage his child and even jokes take on some "parental responsibility". I'm 22 so obviously I have no idea what to do

Now he wants to create a new groupchat with just me and his 10 year old son which is odd to me. He said it is more for me so that I feel comfortable "scolding" his child without the grandparents present. I can't help but feel it is not for me but for himself and that he is trying to hide something from the grandparents.

I put up with this since I am leaving anyway in a few months and the pay and hours is good however has anyone else dealt with a similar situation before? I can't help but feel something is up and that he is trying to make me his child's nanny or something or his PA?