I don't think you're being awkward at all. It's difficult when you have little ones and they can't go and your entire support network is going. We had people not come to our wedding because we didn't invite the kids and I was totally fine with it, and that was even before we had our own baby. FWIW it upset me that we didn't invite the kids - the reception place was charging us full adult prices for all kids over 2 and we just couldn't stretch that far. I'm sure your cousins will understand.
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