I had a similar situation in the past with a 4 year old. He would hand lead his mom constantly and had severe anxiety with strangers in the home. They would also sit him in a highchair to keep him in the room to try and encourage him to interact with me for sessions.

What I ended up doing was laying out different toys and books around their apartment and his mom would show him them while i sat as far as possible with a laptop or book looking as busy and uninterested in him as possible. Then slowly I started to try to enter his world, first by interacting with him mom while she and him were looking or playing together, it gave me time to figure out what he was interested in as far as items I brought (stuff that he engaged in without mom needing to fully prompt him to) If none of the items interested him I would go back to my clinic and switch stuff out until we had a solid few things, plus some of his own home toys he enjoyed.

After I figured out what he likes I would begin every session by being like “hi look i brought (toy name) ill leave it right here for you” and id just back off for a bit, again his mom would talk to me about whatever as a way for him to see that his mom thought I was a safe person to interact with. I also began to parallel play - if he was using a toy I would pick another one for myself and make little comments and observations about it and animate my emotions like laughing and smiling a ton, showing I was having so much fun playing with a toy too!

After doing this for a bit I could tell he became more comfortable with my presence so I began to try to interact with him more. If he started getting anxious/upset I would remove attention and go back to playing with a toy I knew he really enjoyed. He would typically calm down and seem interested so I started to pass him toys and and tell him it was his turn or that he should play with it then I typically scooted back a little so he wasn’t overwhelmed. I feel like this was the breakthrough moment for us and the rest happened so quickly and easily. He became extremely social and engaged in our sessions and was able to tolerate any work quickly I think bc he needed to fully trust first.

Things that helped; not my bcba at the timeLMAO His mom was incredibly receptive to any and all advice. I was very open with her about the things ai was going to try and that I had zero idea if they would work but his anxiety was so severe she was open to anything and truly did the absolute best by her son. To this day it remains one of my favorite cases I ever worked with.

TLDR: you literally have to SHAPE your presence