Kraftmaid has drawers that might suit your design. I found this by clicking Cabinet Specs/: Cabinet Types Furniture Cabinets Furniture Accessories Furniture Drawer 12" H The drawer comes in several depths. I'm sure you can find something similar to this in other kitchen manufacturers' lines. Here is a link that might be useful: furniture drawer

I had the very same dilemma, trying to find a small vanity to put in my powder room (the space had a very inadequate, builder-grade (read: cheap) pedestal sink). We ended up going to Expo Design Center, where one of their vendors (Strasser) lets you custom-design your own vanity, with a range of sizes, styles, door types, stain colors, counter materials, sink types, etc. While this wasn't the cheapest option, it allowed us to get exactly what we wanted. Since nothing "standard" fit the space, it was worthwhile. The new vanity was delivered within about 3 weeks after ordering, and my husband was able to install it within a few hours (including brand new faucet, which we'd purchased separately). I will post a photo later. Here is a link that might be useful: Strasser Vanities

I had the exact same problem. I picked out the vanity I wanted but did not think about the fact that it wasn't made to sit flush against the wall. I spent a month looking for something else, but in the end we decided to go with something shorter and have it not be against the wall. But we were going from 72" to 60" which is probably not workable in your mom's situation. I did find a lot of vanities that did have flat sides and could work in a corner, if you are willing to have the countertop fabricated. They just need to not have any trim detail on the top or bottom like the one you picked out does. I would just look at the ones without the pre-made tops. Because the pre-made top will still leave you with a slight gap because of the countertop overhang. This is an example: Avanity Modero which is sold everywhere, not just at Lowe's. The cabinet we ended up buying is an Avanity Madison which won't work for you, but I assume it is of similar quality. We are pretty happy with it. The drawers and doors have soft close but I do feel like the glides in my Ikea kitchen drawers are better quality. It is very pretty and I wanted a stained wood so I am really happy with our choice. If I had been willing to go with a painted finish, I think we might have stuck with the 72" Modero.

This kind of monolithic wall-hung vanity tops are probably custom. If you don't mind white, look at MTI counter-sinks. If you simply want wall hung and would like drawers, look at wall hung vanities like these at DecorPlanet. I am not saying that these are good quality or not, just wanting you to see them for their style. You can have a wall-hung, minimalist vanity with drawers in it. You can search for wall-hung and modern vanities with the size you need at build.com, Qualitybath.com, and Wayfair, too. Duravit and Nameeks are two European companies that also do wall-hung vanities and counter-sinks.