What is the ruling on attending a family gathering to eat "aseeda" (a traditional dish) and buy toys for children in celebration of the Prophet's Birthday, knowing that it is an innovation (bid'ah)? And should they be boycotted on this day only, or not?

It was previously explained that celebrating the Prophet's birthday is an innovation (bid'ah), just as we clarified the dislike of holding feasts on this occasion. The legal ruling must be made clear to these individuals that the celebration is an innovation. If they respond, then that is well and good. But if they insist, then do not celebrate with them, and your refraining from attending is a practical denouncement that is Islamically required.