It is not a bizare statement at all.
If I were the OP I would not leave my children (esp at that age) for 4 days/nights whilst I went abroad. I would say to the couple, it is your wedding so I have to accept your terms but I'm afraid your terms don't meet my family needs or budget so I am very sorry but I can't come. My husband would love to come but the cost of him attending alone is still too great an amount for our family to bear as it would mean we would forego our family holiday, which is essential to us.
However, I fully accept the wedding couple can dictate their terms - even if those terms affect not just the 10 min wedding but the whole time they are there. It is not to my taste at all, but the wedding (or holiday, whatever you decide to call it) is happening purely because of their wedding, therefore, they have a very large say on the terms of the day/days.
It is up to the guests to decide whether to attend on those terms or not.
If the couple said you can only come if you dye your hair green, so be it. Just say no if you don't like the terms.
My step sister got married in a castle in Scotland about 15 years ago (and they and their friends and family lived in Guildford - miles away). It was a child free wedding 'long weekend'. The whole castle was booked for their wedding and it was a boozy affair. It was sad, but some of their friends could not attend due to childcare difficulties. However, if they had gone but left their children in the room with a nanny, the children would still have been there the morning after, for lunch after the wedding etc.
As I said, not all of their friends could attend. However, she didn't fall out over it. She just accepted that if she wanted a child free weekend wedding then not everyone would come.
The whole point of my step sisters wedding was to have a long weekend in a castle with no children. In fact, she didn't want any parents staying in the castle either so my step father and mother had to get a room in a local hotel. She wanted the castle to be filled with her friends only - not family who tend to row!