Where can I find a way to shower or wash my Mom properly without making a flood in the bathroom?

I think you'll need to talk with the doctor about alternatives. As Pstegman so wisely said, an occupational therapist may be able to help determine the best approach and the doctor should be able to refer you to the appropriate person.

Some modifications may be paid for if your mother is on Medicaid, but you'd have to check with both the therapist and Medicaid to be sure.

Good luck. This is one of the toughest issues of caring for someone with mobility problems.
Carol

Have her MD send in an occupational therapist (OT) who can show you and her how to safely get in and out of the tub. They usually recommend grab bars, a tub rail, a handheld shower and a safety seat. In some cases the tub can be cut lower, but you would have to pay for that.

Also, check with your landlord. You may be prohibited from installing any kind of grab bars (and don't use the grab bars you buy at the drug store that are the sticky kind. They're not reliable and very dangerous. The only kind we used were the ones that needed to be installed into the walls and tub).

Is the bathroom carpeted? If not, you can use a small shower bench that extends the width of the tub. Your mom can sit on the bench and with a detachable shower head you can get her clean. However, you might want to put towels down on the floor (if it's tile) so it's not slippery. It makes a mess but the only other alternative would be sponge baths.

Here is the chair we use it is great... Amazon sells this or you could look other places. Because it has the cutout seat they never stand in the shower.