Definitely check with the countries to which you're traveling. In Ukraine they have the right to ask for a notarized letter from the other parent saying its ok for you to take the baby out of the country.
A friend of mine is from Costa Rica and traveled there without his wife. His DD is very blond but actually really looks like him. They kept him there for an extra day on his return trip until they could get proof that she was his child and that his wife knew bout their whereabouts. I guess child abductions are common there.
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We'd often travel with only one parent when I was a kid. Check the rules for the countries you are travelling between.
I think that it is good practice to bring at minimum a note signed by the other parent identifying you and the kids and everyones relationships, acknowledging where you are going and when, as well as a copy of a piece of their ID.
Re: International travel without spouse...
agreed with pp
I have travelled from Australia to the USA many times with my dd without dh and I was never asked for any paperwork
I think the main issue would be if you had different surnames
I think that it is good practice to bring at minimum a note signed by the other parent identifying you and the kids and everyones relationships, acknowledging where you are going and when, as well as a copy of a piece of their ID.