Switch the door to open out. Get a new white vanity. Paint the walls , medicine cabinet, and ceiling a crisp white. The floors and shower tile are neutral enough to leave as is. (Tile paint is super toxic and might not stand up well.) Have the boys pick out a shower curtain they love. It is easy enough to change as they grow.

I agree with the other commenters about not trying to paint the tile. Painting the walls will change the look substantially, and if the vanity is rotting, surely you need to replace that. A shower curtain will improve the appearance of the room as well. While a lighter wall color would be an improvement, I would be careful when choosing a white. There are a lot of different shades of white. Make sure you choose one that will go with the tile. It probably won't be one with a blue undertone. The tile looks a little pink in the picture. But pictures can be deceptive as far as colors, so I can't tell you exactly which color will work. You may want to look at off whites.

Moving a smaller vanity to wall next to toilet not a good idea- plumbing already in place plus heat vent right there. Impossible to easily clean around toilet. You have two boys! Door opening out, new vanity, over door towel rack so towels aren’t directly above toilet, take out wicker shelf, and more fun paint color will be perfect solution.

IMO bathroom doors should always swing out it just makes sense if you fall and block the door it will need to taken off to help you So change the door direstion the replace what needs replacing . BTW I had 3 boys the rule in our house was if you want to pee standing up you also get to clean the bathroom even my husband followed the rule . Ther eis no reason for men to pee standing up in a home ever .

Some quick and easy steps to take while considering the excellent suggestions above:

Remove the outer shower curtain to reduce crowding. If no one takes a shower in the tub because the kids are still taking baths, you can remove the shower curtain altogether. Put it up again when they are old enough or if you have guests using the shower.

Replace the wicker shelf with a towel bar ($25) at kid-friendly height (about the same height as the vanity) to the left of the vanity. Put a plain wood shelf ($25-$50) above it to store whatever is on the wicker.

Remove the towel holder from the back of the door once you have installed a new towel bar to the left of the vanity. It will remove the annoying flopping and crowding of the towel.

Hang the artwork over the new towel bar and shelf or hang it over the current wicker shelf.

If you want to see if experienced DIYers think the vanity can be salvaged, please add brightly lit photos showing the water damage and rot. Sometimes things can be fixed, sometimes it's time to replace them.

Save your money and redo the bathroom when you can. That vanity is too large for the space. If I was re-designing, I'd get a smaller vanity and put the toilet in the corner on the same wall as the sink.