My kids were born Dec. 27, Jan. 15 and March 6.
For the 2 older ones (January and December) we combine the family party. We are far from the relatives who want to come (closest ones are 1 1/4 hours away, farthest ones close to 3 hours away) so we only ask them to come to our home ONCE in the wintertime. The little guy gets his own party in March.
The Big Kids have always shared a party and they don't mind. Last year we let them have "friend parties" separately. But at the joint party we have 2 cakes, 2 sets of plates & cups....Barbie and dinosaurs coexist quite nicely at our parties

Since we are so far away from everyone, the kids are just happy to see their cousins and other relatives, and they don't mind the 2 cakes, 2 songs, etc. It's just "how it is" in our house. I don't think they will grow up emotionally harmed by it