*Yes, your SILIL does not sound like a Nice Person to intentionally book her wedding knowing that you are planning a family occasion the same date, knowing that a) birthdays cant be moved and b) family cant afford to do both even if you move the date and c) that attending a family wedding will trump a family birthday, even if its a 'big' birthday
And then i'd guess that if you did hold it near the wedding venue the evening before, dd's friends couldnt come.*
Whoever this was got it in one. 
Yes, Americans are nut-tastic about traveling to weddings/parties/things, and as long as I've been alive (43 years and ticking) one's sixteenth birthday party has been...well, not as big as eighteen but definitely occasion for a larger party than usual. I'm not talking about a big quinceanera ball-style party, with foofy gowns, tuxes on boys, and that, just a large group of both friends and family she loves but seldom gets to see. Oh--and that being Memorial Day weekend, we nearly always have a BBQ that weekend and more often than not, PILS and PILS2 attend. If we did it near the wedding venue that would cut out all DD's friends and my family, for whom instead of driving five hours it would mean driving eight and a half. And oh god NO the party is going to be NOTHING like that. Just a lot of friends and family in the upstairs, cozy room of a local pub with catered food and some music to hang out by. DD is not into the Big Foofy Dance thing in the slightest.
However, SIL2B did me a bit of a favor by making the wedding under-18 so obviously I can't go as I'm not leaving the kids by themselves over a long weekend at 13 and just-under 16. Was having a bit of a vent, mostly, over how A did that thing she usually does over the past nine years I've known her (thinks only of herself) only this time is the first time it's directly affected me. As for the 'how do you plan that much in two days' it's not really the wedding she has to plan; every conversation with her for the past few years has been about how "D and I have decided for our wedding..." while D stands by with a mildly embarrassed look on his face. She's been planning Her Perfect Wedding since she was, like, six years old.
On the MIL2 thing - she really is like a second MIL to me, the families are that close. All four of the ILs have been friends since before DH was born. Four kids in MIL's family, three in MIL2's, and they were all raised pretty much next door, all their lives, as siblings. I'm Aunt Merry to MIL2's grandkids as well as to MIL's.
Just heard from DH that MIL is narked off about the wedding date too. DD loves all of her grandparents and, as the party is going to be a family and friends party, yes is going to miss them being there. I haven't decided what to do about the party yet. I can't hold it much earlier in May because the restaurant gets booked up tight for college graduation/new-doctorate parties. Much later and the kids will be out of school and off on vacations. Going to have to have a think about when to have the party but, in the meantime, since DH will be the only one of us going to the D&A-stravaganza, I'm going to have to demand he take good notes!!
Oh--and yes, in the US your licensed officiant comes to you and not vice versa. She's having the ceremony in...what I guess is called a Stately Home over there, at 2pm, and then (quoting from the computer-printed cut-out Save the Date card) Grande Reception Ball at 5pm. Nothing in between, nowhere to hang out in the vicinity. So, a bunch of people hanging out in their finery with their thumbs up their butts (figuratively speaking, haha).
(Also, not a wind-up, penis beaker, naice ham, Korean lady, and not a reverse IABU.)