Apologies - I've not read all the replies so if I repeat what everyone else has said, ignore me.
I think the issue is that you're simply being told you're not going along, that only your DH is being invited and his trip is being paid for. That would stick in my craw.
You and DH are a unit. You should be considered together as a unit.
It would have been different, wouldn't it, if you'd been told by your DH "Mum wants to go to NYC for her 60th, but she only wants FIL, me and DSis to go with her. She wants to party it up in NYC with her husband and her kids. I know that's not entirely fair to you, as I get to piss off to NYC for a week of fun, while you're being left at home, literally holding the baby, by yourself for a week. I'd really like to go. What do you think, given that it's a one-off for my mum's 60th. To make it fair, when I get back, we will arrange for you to have the same amount of time off to go and do something really fun and I'll stay home with the baby."
But it doesn't sound like that's what you were told.
It sounds like you were told "that's what Mum wants, that's what she's going to have, I'm going, you're not, deal with it, by yourself, at home with the baby, for a week".
That would have had me livid, too. So, if I've got it right, YADNBU.