They're both grammatically correct, but sound weird. "I sat down in my seat" sounds a little weird. I would take out the "in my seat" if it's already implied. "I seated myself in my seat" sounds really unnatural. "I seated myself" sounds old-fashioned, and you'd probably see that mostly in books. Again, the "in my seat" sounds weird. I would just say "I sat down". The context will usually tell you that it's your seat that you sat down in. For example: "I walked into the theater. It was dark and cold, but I was excited. I sat down, and put my purse on my lap." Even though the seat was not mentioned, we can all assume that she sat down in her seat. Hope this helped :)

to sit- the physical act of sitting down to seat - to provide a place for someone to sit Technically, they're both legitimate sentences, I think. However, I much prefer I sat down in my seat. I don't know that I've ever heard someone say I seated myself in my seat.