I’m not WVMomof3, but I hope you don’t mind me chiming in.
My info is several years old now, so take it with a grain of salt. I used to stalk the website multiple times a day, and at one point I’m sure I had reservations for three different places for one night until I was able to get exactly what I wanted. One thing I found was that on the Xanterra site, there were two separate ways of checking availability. Sorry, I forget exactly what they were (maybe by lodging versus by date), but one day when I released one of my nights and then shortly after checked availabilities, I noticed my released room showed up on one way of inquiry before the other. Maybe if that’s still the case and you can figure it out that will help you get what you want.
I just checked, and unfortunately, Grant Village is closed. It’s out of the way, but that was the easiest (and first place) I was able to secure a room. I started with that and then shifted things around as they became available. On the plus side, I noticed that a couple of places didn’t fill up last night, although they did today by shortly after 10 am.
So...we stayed in an old room at the Old Faithful Inn. We only stayed there one night, because the bathrooms are down the hall, and I wasn’t sure how that would play out with a teen daughter,but we both wish we had stayed there again rather than the Snow Lodge Cabins we stayed at when we completed our loop around the park. We were urged to stay in the old rooms by multiple people on Tripadvisor, and I’m so glad we did. It was our favorite. Just so charming and felt like we were having “the Yellowstone experience.” On the other hand, the Snow Lodge Cabins were our least favorite rooms. I complained and got a small credit to our bill. The carpet was dirty and gross. Of course, that may not be the case now.
Our second favorite were the Canyon Lodge Cabins. A much nicer room than the Snow Lodge Cabins, and with a family, you might appreciate the size over a regular room.
We stayed at the Mammoth Hot Springs Hotel also. It was fine for what it was, just not my favorite. They were just finishing up a remodel, and the lobby to me had no “ soul.” The room was small, but fine.
We didn’t stay at The Lake Lodge, but we did stop in there, and the public spaces and grounds were very nice.
Hope this helps.