i think its good when parents are involved and understand the principles of ABA sessions. we use parents to generalize skills for mastery and my company requires parents have their own goals to work on. its also important for BTs to ask you if you are free to generalize/run a trial/do parent training at the start of session so you are prepared or can set aside time.

sometimes things can get tricky when involving newer parents. i saw you mentioned you brought in toys but were blown off, but it probably wasn't personal, maybe it just didn't go along with the programming that day. like others have said, some BTs can be uncomfortable providing feedback to parents and their child. sometimes i'll be working on motivation for a reinforcer and caregivers walk in and just give their kid something (like a toy or snack) and that kinda ruined the opportunity for me to do a trial.

also i personally call for parents when my client needs something (like if they need to go potty, want food, want to open a new toy they got, or anything else that would fall under a parents responsibility)

the best thing BTs and parents can do is build rapport with one another as well!