They don't have the right, but it's not your problem. I can see being annoyed, but there's nothing you can do to stop them, and it's not your event, and you won't have to cough up the extra money for their presence....just make sure you're not trapped into babysitting the little angels and it should be a wash. :)
I can kind of understand the one who's standing in the wedding, because she can't "not" show up and she may have extenuating circumstances or whatever. I do not condone, but can see, how the other decided "well if she's bringing her kids, I'll bring mine". What people don't get is that kids don't LIKE weddings. Not many children enjoy being dressed in stuffy formal clothes, sitting still, being quiet, being bored while adults do adult stuff, and then staying up past their bedtime or missing nap but expected to act like little angels. So why NOT just make arrangements? There's a few options that I would take if in this situation (not just for you, but for the other women involved as well):
#1 would be that my whole family takes the road trip (you said it's driving distance), and we do our own thing. When it's time for me to get ready for the wedding, husband can take the kids to the park, Chuck E Cheese, a movie, "whatever" there is to do around there. The invention of the internet, combined with the wonder of mapquest and gps, make this so doable. While family is in town for the wedding, if there's someone your family would like to spend time with (a grandma, aunt, whatever), take advantage of being in the same town and do something with them as a family before or after the wedding hoopla.
#2 would be that even though the bride/groom are busy, there must be someone there that can give you a reference for a good babysitter (or sittercity.com) and you could even SHARE a sitter with the other wedding kids. I have done this before, through sittercity.com, so that you could know that the sitter was prescreened, had the background checks, you could read their references, read their little blurb about themselves, talk to them on the phone. Then all can go to the wedding (the weddings I have attended in the past were just a few hours, max...not much different than going on date night or whatever).
#3 What you're doing: father stays home and watches the kids and you just go up there alone.
THIS kind of b.s. is why we semi-eloped and only took mom, dad, brother, 1 aunt, and BEST friend to our wedding. Blech. Don't just assume that the bride/groom are ok with the way these other 2 are acting. They could be aggravated, stressed out, concerned about how these kids will change the "vibe" of the reception, you don't necessarily have any idea how they are feeling about this. They may be giving in, grudgingly, because they feel that noone will listen to them anyway, or they can't control the situation without a family feud, but that doesn't make them happy with it or mean it's a double standard. It just means you have the class to go with what was requested of you for this party.