My husband's family is like this to an extreme, he even goes to his cousin's kids' birthday parties. My family is too large, I have 29 nephews/neices and great-nephews/neices, and we stopped this long ago. We don't do gifts with each other either. I do send them all birthday cards, but started doing that once I was in a position to do so (like my mid-20's), which means that half of them didn't get cards until they were in their 20's, haha.
In addition, for our son, we don't invite family to his parties. His first was grandparents/uncles/aunts only (that alone was 28 people) and every party since was a pajama fundraiser for homeless children. The grandparents were told about the event if they wanted to stop by, but they chose just to come over for dinner on the actual bday.
Good luck!!!