Okay, so why dont you do something about this situation? Like for instance, if she wants you to send her family presents and call them for their birthdays…simply say you’re too shy or not good with dates. Why doesnt she wish them on your behalf? I dont just say Happy Birthday to someone and be done with it, I always include my husband and say its from BOTH of us…even if he said no such thing. Unless its your MIL, FIL, SIL or BIL…I wouldnt worry too much about extended family and cousins. You can call them out of courtesy but you’re not required to send all of them presents!
Teach her these things by doing them yourself. If there is some sort of a birthday, anniversary or event coming up in your family, tell her you gave a present or wished someone on her behalf as well.
Regardless, you’re just going to have to make sure you dont become part of this bloody war between the inlaws by taking anyone’s side openly. Be just, be fair and most of all…stay away from the petty arguments!