I would want the children to have the same last name as me as well. And as previously stated, when travelling, it certainly would make things a whole lot easier.
My mom shakes her head - these weren't even issues when she got married!
I don't mind paying for a second bag on the way down, but I don't want to have to bring it home. I would plan on using a duffle like bag to pack clothes in on the way down, and either leave it there or pack it in my suitcase on the return.