It's not really a "normal" relationship when your relatives are proselytizing to your kids. It's not as if they're reading harmless bible stories to them with nice messages behind them, like fairy tales. No, they're filling their heads with typical JW judgmentalism, intolerance and fear. I wouldn't stand for any babysitter, relative or not, preaching any religion or telling my kids to judge me or criticize what I do or don't do. That's just not on.
Years ago, after I'd been out of that cult for 8 or so years, happily married with 2 kids, living a wonderful cult-free life, my JW mother suddenly decided to stop shunning me. Probably due to the grandkids so I thought why not? It didn't take long before she sweetly suggested my kids needed religion in their lives. I practically exploded. It was absolutely NOT okay to have my kids be exposed to that cult's hateful dogma. I pictured exactly what you just posted - my kids' heads being filled with intolerant crap that made my husband and I look poorly and made my kids' view themselves and our family life with disapproval and guilt.
We didn't have a "village" when we raised our kids. It was hard but I'd rather not go out on dates than risk my children being brainwashed and turned against their own parents or made to feel guilty and less than adequate.
What I did was I very clearly, very firmly told my mother to not ever mention anything about her god or she would not be welcome in our house. It was harsh but I knew I had to be that way with her. If I was wishy-washy about it, she wouldn't have respected my stance.
They don't need to get mixed messages and feel bad about the everyday fun things us free people do and enjoy. What happens when Christmas comes around and they're all happy and excited about it? They don't need interfering relatives killing their joy and making it look like you're doing something wrong by celebrating it.
If I were you, I'd tell your rellies to back off with the religion. After all, if anything makes you feel uncomfortable, you don't have to put up with it, they're your kids.