I would be furious. I get that some ppl chose to have no kids at their wedding and it's their choice. But I would be livid that nieces and nephews are not invited to a destination wedding. In your own town/city then it's reasonable to think a babysitter could be rounded up.
My bil and sil wanted a kid free reception at a destination site but yet dd1 was a flower girl. Dh and I had only dd1 aged14mths. I said that if dd1 wasn't invited to the reception there was no point me flying down at all. Dh also then declined to go. They had to back track as dh was a groomsman and mil and fil were furious.