All families are diifferent and give different importance to things like birthdays. We make a big deal about my kids birthdays, but no so much about our own and we often get cards and gifts for the kids late and tbh I am not so religous about making sure that my neices and nephews get theirs on time either. The kids quite like getting a late present. Appart from their 1st birthdays, my mum tends to not come along to the kids parties as she sees it as a party for the kids and their friends, not for her.
I don't find that upsetting in the slightest.
Your partner needs to get a grip and realise that not rushing across to see your child on her birthday, doesn't mean to say that they don't love her, they just attach a different level of importance to such things. Do they treat your sisters kids any differently?
Maybe they are thinging practically that as they are busy orgainisg the party and that they will see you on that day, there is no point coming across now and she will get her presents when she sees them.
You are in danger of making a full blown family fued about something that they probably don't see as that important. You could try explaining your feelings to them, but I bet that they will probably not even realise that they are upsetting anyone.