What should I do, as I have forgotten a vow I made for my son's recovery from cancer, knowing that I believe the vow was to hold a dinner banquet, but I am not certain?

A previous fatwa clarified what a person who made a vow then forgot it should do. Scholars have two opinions on this: The first is that he should investigate, and if something becomes highly probable to him, he should act upon it; otherwise, he should perform all possibilities to fulfill his vow with certainty. The second is that he should offer an expiation for an oath (kaffarat yamin). So, as long as your strong presumption is what you mentioned, then do it, and your obligation will be discharged thereby.