Palau Pacific is definitely the place to take kids because it has the only proper beach of any resort/hotel in Palau. Very nice, right in front of the hotel. Your kids will meet other kids there, too, and it's very level so good for your mum. Excellent food, too. Local dive op is okay, but I'd also go diving with Fish n' Fins. They'll pick you up. Only downside is that the resort is far from town, but it's a short drive or cab trip if you want to wander around and go shopping.
Blue Corner, Jellyfish Lake, etc. are all a good half hour boat ride or more, depending on conditions, but that's the case from any land-based op in Palau. You have to hike over a hill from the landing to get to Jellyfish Lake, so be sure to wear good walking shoes.