my ds is 8 now, but when he was 4, we visited my cousin whom i hadn't seen in a looooong time. she and i were very best friends at 17, and this was 4y ago when we were 45.
i'm very much Pagan, and she's now very much Christian of some sort. she goes to both Episcopalian (in which we were both raised, separately, but her brand now is much more evangelical/fundie/something) and...i think Presbyterian?
but at her house i was surprised to find God songs in the CD player all the time, etc. she was VERY much into it.
anyway she told me before we got there that she was involved in the VBS and we could go or not go, but that she was committed.
so, we went. ds participated. the whole time. i went in once, and was pretty mortified. it was partially like a camp, with tents and stations for crafts and stories and fun things, but there was one part at the end of every day, where everyone gathered in this auditorium and got led in Jesus songs, with a screen backdrop with pictures on it, and words to the songs for them to follow, and leaders up front with identical camp shirts and too-fake pasted Barbie smiles.
and they'd every now and again shout things like "who loves Jesus?" expecting the crowd to yell answers, just like in a regular camp, call and response.
it was awful-- for ME.
i did not really want ds to be involved in this thing, but i didn't want to insult my cousin, i was btw a rock and a hard place-- but in the end, ds didn't at ALL get anything about Jesus or God or anything. at ALL.
it was a zoo or jungle or some animal curriculum that year.
he got to tie-dye a shirt and print animal stencils on it, and he had it for years.
anyway, that said, i would not do it again, because of MY comfort level, but it was harmless in hindsight. as i hoped it might be in the moment.
BUT. here are more hindsight thoughts. how often do you/your kids get to visit the grandparents? is it more important for them to do VBS than visit with you? can't they wait a year? if not, if it IS that important to them, then consider what they might have in mind for teaching the kids...or how much you want them to be involved. or, judging from what i and others have said, if you care

i am a Pagan and i am also a UU. our church is really awesome because in the RE (religious education) they do teach about many religions-- better than i could do it. and there is room for athiests in the UU. there are some in my church. though i do admit it's kind of weird, like a PP said, if you don't find your niche; it took me awhile to figure out what it was all about, there. they ought to call it Salon and not Church, lol; there's no gods mentioned except in historical/prophetical context, it's very intellectual, and i think the only thing missing is lots of coffee and cigarette smoke

well, wasn't that off topic


sorry!
anyway, OP, i hope you find a solution. let us know how it goes!