I don't think it is a problem if you are very careful. Carefully check the specific airlines rules and bring the largest carryon and personal items they allow (even for the children). Additionally, I have never seen the airline stop anyone with a carryon, personal item and a water bottle over the shoulder and a reading book (no need to pack the water bottle and reading book).
Most ships also provide laundry service. On long (eg, greater then 2 weeks) land trips I figure on at least one laundry.
Also, think about what you can easily buy at the destination in Europe so you don't have to pack that item, just buy it there. In the alternative, check one item of luggage for the whole family with the assumption that it will get lost (pack only items you might want to have but can get away without and don't cost much to replace) in the worst case scenario you won't have the optional items and might have to file a claim with the airline.