I don't think you are looking for a fight at all, you have a legitimate gripe on several fronts.
I think to boil it down, I agree that you should look at what generations will go, regardless of age. However, it would bother me beyond belief to not be involved in this decision yet be expected to foot half the bill- unacceptable on SIL, just wrong.
I would try to be civil, but be matter of fact in approaching SIL. Simply saying "let's hash out this guest list and what WE want to do in terms of kids." If she says that she already decided, politely say "oh, I'm just wanting to make sure that since we're contributing to this event that our feelings are considered." If she balks at that, then it's bad on her because you kept it on the up and up.
Again, I do feel like ultimately it's fine to keep it generational. If you really feel like age is the relevant factor and that your grandkids should attend, then fight for it- you are paying for half!
Even if you decide to not have your grandkids attend, at least you have made the decision together and had your say, and find ways to point that out. I am a believer that you teach people how to treat you, so draw the line so SIL knows. You are handling this nicer than I would, and you can certainly hold a boundary without being rude.
I think you are just trying to have your say, not picking a fight. Good for you.