Those of you who do not see
manipulation written all over this have obviously never had experience with a Master Manipulator.

Those of us who are saying, "Oh yeah...MIL is definitely pulling a power play," can see it a mile away because we've BTDT. Poor thing....Pity your DH hasn't wised up to Mama's puppet string-pulling yet. It certainly helps when they learn to see that the Empress has no clothes.
Oh well....Tell MIL that you're sorry but that you had already realized what a PERFECT situation this year was, what with DD's b-day falling on a Saturday and all. You'd be able to have her party on her actual b-day
and it be a convenient weekend, plus not have the problem of the 4th of July weekend. So you'd already had that time set aside. But they are more than welcome to come over to your house.

Come on, the world's not going to come to an end if she doesn't have you over for barbeque on the 12th of July.

You truly need to draw a line in the sand on this one. Really, the sooner the better.
MIL was put on notice early in our marriage that if she tried this crap, I'd come up the winner. Up until I came along, she was always the queen and her tears, fits and tantrums got her way every time. Then she met someone who didn't give a rat's hiney about her tears, fits and tantrums. Me. I stood my ground, she was forced to back down, and our lives are soooooo much easier than if we'd given in. Yes, she resents me, but who cares? The Queen was dethroned and it was about time.

It's time for a coup in your family, IMHO.
