what's the size of the closet? To start - remove the pole and shelf - how much space is on the sides?

First step is to remove the doors. That will give your mom a lot more elbow room. Take out the lower shelf.

If this is functioning as a vanity too, next step is to hang a mirror on the back wall.

I would leave the bar, and hang a closet organizer from it for storage of everything that would normally go on a vanity top. A narrow shoe organizer would work.

Invest in pretty baskets or boxes for the linens. Roll them in logs and stand them on end.

Enjoy your time with your mom, I know it's hard to support loved ones through an extended hospital stay. It's so sweet of you to have this space ready for her. Keep focused on the fact that she is more happy to be home with you than to have this space! Don't let it worry you too much :)