My cousin is the president of the union for the border guards. I asked him what happens when you cross over. When you cross the border they scan your passport for warrants, etc. Nothing comes up about children. My cousin said if you have supporting ID you will not run into a problem usually unless you get an idiot guard crossing into the US. I questioned all the single ladies out there that are divorced, went back to their maiden names but have kids with their husband's last name. He was kind of stumped. There are a lot of different scenerios out there as to why the mother wouldn't have the same last name as her children. It must happen all the time. Divorced & remarried, never got married but live commonlaw, death, etc.
I have 4 friends with kids now that are married & have no intention of taking their husbands name. You do not have to take your husband's name, it's totally optional. My GF has been married 30 years, has 3 grown children now, & has never changed any of her ID. They travel abroad constantly & always have & she said she's never run into a problem.
I go by my husbands last name now just for the sake of my son, but I honestly don't care to assume his name on my ID (you never legally change your name when you get married, you just assume the name, if it were legal, you would have to pay for it & it's a pain in the butt, my cousin tried it.)
So just because your ID/passport has different info than your child's I wouldn't sweat it. My flight is always under a different name than my son's, my health insurance, everything. No one has ever said a word to me.