I had to do the same thing when I got my oldest son's passport this year. My ex and i weren't married when he was born and even though we all have the same last name, I had to get his long form birth certificate.
On a side note, I found it amusing that nobody asked any questions of myself or the kids when I took them from Canada into the US but we were checked coming back. The border guard talked to my oldest and asked him who looked after he and his brother and sister, whether his dad knew where they were and if he was okay with it. I thought it was funny that it wasn't until I was bringing them back into the country that they were questioned. I wasn't worried since I had a notarized travel authorization from my ex and our Separation Agreement stating that we had joint custody. I offered the authorization to the guard and he said they usually only check those when the kids are small and non-verbal. Once they are older as my kids are, they usually talk to the kids themselves and ask questions.
