Honestly, been there and its such a headache when everyone buys the same thing. I have tried pretty much every app out there because my family is huge and nobody communicates. Giftster is basically the gold standard for this exact situation. It looks a bit old school but it works perfectly.

• Giftster: Its free and lets you create child accounts so you manage the lists for all 3 kids. The best part is the claim feature where people mark things as bought, but it stays hidden from you so you dont spoil the surprise.
• Elfster: Mostly for secret santa stuff but their wishlist feature is actually really solid. You can add links from any site and people can reserve items.
• GiftHero: Super clean interface and works like a browser extension. Ngl, Giftster is probably your best bet for the MIL situation since its hard to accidentally delete stuff on there compared to a shared note...

Regarding what #1 said about it being a headache when everyone buys the same thing... yeah, I felt that in my soul. A few years back my aunt bought the same Lego set as my husband and the look on his face when he realized he had to return it in a snowstorm was enough for me to switch. Over the years I've probably cycled through a dozen different apps trying to find one that my tech-illiterate relatives wouldnt break. I totally agree that Giftster is reliable, but Elfster is what we have used for the last few seasons. In my experience, its way better at handling the surprise element. When someone marks an item as bought, it hides it from everyone else and you can set it so you dont see it either. I also swear by using my favorite gift list extension when I am browsing to just click a button on any store page. Saves so much time.