The boundary waters area is really great, but maybe not for a family. Honestly, I don’t think any of these areas are going to compare to Yellowstone in terms of the purely sublime combined with ease of access with children.
New River Gorge is nice, but, like a lot of these options, it’s “take your kids for a weekend” kind of nice, not “my mom is paying for a multi-generational meeting at a national park visit” kind of nice.
It’s all what you make if it though. Were I you, I would figure out how to go to Yellowstone. Especially considering it’s the preference of the person, you know, paying for it.