Oh frick, that's a tough one. No matter how you play it, you're the bad guy :-( (By the way, I completely support your decision; I wish more parents would trust their guts when something pings their hinky-meters).
I don't suppose there's any chance there's something concrete in his past you can point to? (arrest/convictions, even about something only tangentially related to pedophilia).
What will your mother do if you simply tell her, "Mom, I'm not comfortable with John. I don't know why, but something is pinging my radar. I have to put my daughter's safety first, even if I'm wrong, even if it means hurting you. I'm sorry, and I love you, but it's not a risk I can take as a parent."
Is it "never leave her alone with stepdad" or is it "Never leave her alone with mom and stepdad"?
Holly and David
Adaline (3/20/10), and Charlie (1/26/12- 4/10/12) and our identical twins Callie and Wendy (01/04/13)
I don't make excuses, I just always suggest all-together types of activities and pass on the others, say 'I don't think that works for us' or 'we can't do that' (leaving out that it's 'because I don't want to').
If you look at past threads (probably in general parenting, or life as a babe/childhood years) you'll see that this isn't unique - a lot of others struggle with grandparents who seem to insist on having alone-time with their grandkids instead of spending time with the whole family too. And, likewise, there are a lot of grandkids out there who don't really do alone-with-grandparents sleepovers/weekends/etc. at young ages like your dd (or ever, sometimes). It really isn't even the best idea for some kids, regardless of how parents feel about the relatives. Heck, I didn't do anything of the sort until around 12 or 13, and probably only 1-2x at that (I did have long distance grandparents and extended family members, so that limited it too I'm sure).
Some gentle things you could point out - did you (as a child) have the same kind of time alone with your gp? And at these ages?? If not, remind your mom of that sometimes when she presses the issue. She may have felt similarly and have forgotten what it's like having a young kid.
All-together family time is nice because young kids don't always remember special things they do with their grandparents - and then they'll be more likely to have stories about it from their parents, or pictures their parents took of that time. And that's a nice thing.
Being really regular about sending/emailing photos/videos can also really help satisfy their 'I must always know what my grandchild is doing' without always having to be with her/you. Maybe step that up a bit for them, and it will help their always needing to see you too.
^^In the OP's shoes I wouldn't leave her with mom if stepdad is anywhere in the state. Mom presumably trusts him and might leave kiddo with him.
I have no advice on the actual issue. Drama may be unavoidable.
Keep saying you like spending "family time" with them, and that you like to be there too! When they point out that you leave your daughter alone with other people, dismiss that. "Oh, they're just babysitters!" you say. "But you guys, you guys are family and I want to have a relationship with you too!"
It might work.
Do they already know that you leave your dd with other people? I have pretty much never left mine with anyone (although my older is now almost nine and he's done playdates and such, but not really babysitting situations). I could say to my mother truthfully that I don't leave him (my little one) with anyone, and that I'd like to be there when she's with my older. I don't leave them with their other g'parents either (though it's more bc I'd like to be there, too). But even if I couldn't say it truthfully, I would see it as one of those white lies that is necessary. I really don't like to lie at all to people that are close to me, but saying that you think your stepdad might be a pedophile is one of those things that will most certainly lead to pretty terrible feelings.
Jayne, sewing up a storm mama to ds1 9/03, ds2 2/09, and 2 sweet furbabies.