Upvote:1
No, it's very unlikely to cause problems. There are three different nationalities in my family, we've traveled extensively with various permutations of them including the kids having different passports from the parents, and nobody at an airline or Immigration has ever even asked a single question about it.
Caveat: things may be more complicated if there's any reason for Immigration to suspect that you're not the child's parents and/or there are potential signs of child trafficking (see under "Trafficking Indicators"). But if the three of you are traveling together, the child shares your last name and looks related etc, this is very unlikely.