How can I get my mom to shower and stop playing with her poop?

It sounds as though your mom may be afraid of the water. This is common with dementia pts. Do you have a shower chair for her? Do you use a bathtub or shower stall? If it is a bath tub try sitting her on the shower chair and putting a few inches of water in the tub and using a cup to slowly pour water over her. This is less threatening than spraying her. If it is a shower stall, have a hand held shower and turn the water on slow and let it gently run over her. Don't let it spray in her face.
As for the poop problem, adult diapers and supervision is all I can think of. I hope this helps. Good luck to you dear.

Today I found out (after checking my dad into a skilled nursing facility for rehab) that elderly people only need to fully shower 2-3 times a week. Their skin has less oil and it can actually be harmful if they shower daily. I'm not sure how I feel about this because my dad reeks after 2 days, but whatever. Maybe she is feeling too dry or uncomfortable from daily showers? Try a couple of times a week instead. I'd also invest in lots of antibacterial soap or maybe tell her that if she wants to play with poop she has to wear gloves. Then go thru the motions of putting rubber gloves on her, and keep reminding her- it might take whatever fun she sees in it away by allowing her to do it.