Am I reading this correctly? Your W went on vacation with OM and his children and used the money that was allocated for a FAMILY vacation?
File for divorce while she is gone. Better yet, have her served while she is on vacation. Ask for full custody, child and spousal support and keep the family home.
My H did the same thing (took off on a vacation with OW with our vacation money) except I didn't know he did that until after he was gone.
I don't have children and I know many here know better how to handle these things but I would say "kids, I can't speak for your mother and you will have to speak to her about her actions".