Every year, my partner of a decade and I have Christmas with her family. My family is Jewish and we also spend at least one night of Hanukkah with them. For all gatherings (including birthdays) the gifts are almost exclusively chosen and purchased by the one who is more directly related to the recipient. It always feels a little weird to me that their family gets me gifts, but they never receive anything exclusively from myself, it’s just very vaguely implied that the gifts are from us as a couple. To be fair, their parents give gifts as a couple (always from their mom). Also, I would never ask my partner to purchase gifts for my family in addition to theirs, they’re already stressed enough by finding something for their own family. I’ve never brought this up with my partner as I don’t want to make them feel either obligated to or guilty about implicitly declaring that they don’t want to.
Yes. We buy something for each immediate family member on both sides. Although to your point, my spouse generally takes the lead on presents for her side, and I for mine, but we do actively consult each other before anything is bought, so it does feel like it’s from “us” and not her with my name on it also or vice versa.
I also will generally buy each of them a small gift myself each year (that they get at Christmas) if it’s something that I think they would like or fits their character. Think like t-shirts, trinkets, ornaments, or stickers and the like, and never with the expectation of receiving something in return.