My Mom won't or doesn't remember how to push when she doing a BM. What to do?

Sitting on the pot for hours will harm her tissues and encourage hemorrhoids.

Make sure she is taking in enough liquid. Dehydration will stop you up pretty fast. Make sure she has enough fiber in her diet. Fresh fruit & veg or a supplement in water like Citracal or Metamucil. You will have to get creative to increase fiber and water intake when she probably doesn't want it.

Today, right now, call the doctor and ask what to do. Do not give her Colace or any other stimulant laxative unless the doctor says OK. Ask about an enema, glycerin suppositories, and probiotic supplements to keep things moving down there.

Her level of activity will have a lot to do with this. If she is sedentary, that will slow her bowels as well.

I am willing to bet she has an impaction now and when it dislodges you will want to make sure the house is covered in plastic. There can be softer/runny stool behind the impaction and she may complain of diarrhea because of that, but it is not diarrhea. It might be smart to get her in Depends garments and to never let her sit on anything that isn't covered with an absorbent disposable pad.

This kind of thing can require a lot of patience to see through, but don't give up.

Prunes! If she hates prunes, offer dried Apricots, they are yummy and they soften the stool. Get her to go for a 5 minute walk after meals, it keeps the gut moving.

This is our problem too. The only thing that works is to keep the stool soft so that there is no pushing required. As sandwich says, it's very important that she drinks enough.
Changes to her diet like adding prunes or fiber may be enough, if not definitely consult her doctor before adding in stool softeners or laxatives. We had good luck for a long time using polyethylene glycol (Miralax) daily.
And keep her on a schedule, encourage her to try to go at a set time each day, after breakfast is the usual suggestion. We've reached the point where she is now totally incontinent, but I would rather be cleaning up messes that dealing with a constipation or a blockage.

She's not constipated, she takes fiber everyday, and has a great appetite for plums/prunes, watermelon, veggies, dried beans etc. She won't push to urinate either. I'm sure she could drink more fluids if she would. She rides an elliptical bike every evening, that moves her legs and arms. She has a standing frame to help with standing. She exercises everyday. When it comes bathroom time she refuses to push. She thinks it's suppose to come out on its own or she wants me to get it out. I think she's through and more comes out. I wipe and wipe and wipe. She can go, she chooses not push. The dementia is probably playing a big role in this problem. She won't do it in a diaper, she wants to go to the bathroom. She thinks it should come out on its own!!!!

To put it bluntly, you may need to get it to the point it just runs out. The fact that the toilet paper is coming away soiled tell me that her rectum is probably full. How often does she go, and is she ever really emptying her bowel? My mom can't push and has absolutely no sensation that she needs to go. We have gone through h*!! with this, from laxatives to suppositories to digital stimulation. Believe me, it's no fun for either of us and we still have episodes where she has gone far too long without emptying her bowels. Of course your mom doesn't want to go in the pull up, and unless you are crazy you don't want that either. Unfortunately if you keep her BMs solid enough to prevent it you are probably going to continue having this problem.

My mother forgot how to push also. She had AD. Her nurse started her on "ClearLax" which, along with water helped it naturally just "fall out". However, that means it could just fall out at anytime so be careful!

I will agree that you need to work on keeping it soft enough to just come out on its own. It's a fine line and may have to be adjusted every day. A stool softener may help. Key is drinking enough fluid to keep the stool soft. Be careful with fiber supplements. They can cause pain, gas and bloating if there's not enough fluid. We use Miralax on an as needed basis, with stool softeners. This is all in addition to fruits and vegetables. Bran muffins may help. I hear Date Nut Bread is good. A hot beverage (coffee, hot chocolate, tea, cider) with breakfast may help get things moving.