Well my daughter just turned 1 on 2/26, and we're not going back to Disney till 4/18, but we will be there for her 14 month birthday and I plan to get her a cupcake! But I'll answer what we did do since we don't live near our family. We had a small party at the Rainforest Cafe (can't fit people in our home) with our close friends and their kids. My mom came down, but that was it. Other family wanted us to come back to my mom's house and have a party there, but we did what we thought was best.
Anyway, not that I've been in this situation, but my suggestion would be to have something small at home either before or after his birthday. Invite your close family over and let them watch your little guy dive into his cake (which is probably what they all want to see!). That should appease everyone, and you can keep it really cheap, just getting snacks, finger foods, and the cake. Or maybe even just a cupcake for the baby, not a full cake.