My big issue is trying to change my mom’s Depends when she’s had a BM. Any tips?

What I did with my husband who was completely bedridden, was have an aide come in the morning to put my husband on the bedside commode, where he would then poop, and then she would lift him off(using a gait belt of course) the bedside commode and hold him, while I cleaned him up. That worked great for us, and thankfully my husbands body got used to the morning pooping schedule, and on the rare occasion that he pooped later in the day, my son would come after work and again hold him up while I cleaned him up. I found that way much easier than trying to clean him while lying down.
Also you can just rip the Depends down the sides, and not cut them, but like others have said, it's probably time to use the diapers with the tab closures.
I wish you the best.

First thing. Stop using incontinence briefs that have to be cut off. Pull-ups are for people who are still able to use a toilet. It sounds like mom is past that stage and this product is no longer suitable for her needs.
She has to go into actual diapers now. Ones with tabs so they can be put on and taken off without her standing up and without you cutting them off.
Second, stop trying to toilet her and change her in the bathroom. This is a dangerous situation for you both. Now it's time to change her while she's laying down. This will be far safer and easier on you both. Have her lay flat on the bed with a bed pad or a large towel under her. After you have her clothes removed unfasten the tabs on both sides of the diaper. Starting at the end farthest away from you, roll as much of the soiled diaper under her. Then pull the diaper out and wash her up.
Prepare another diaper by rolling it tight about halfway. While she is on her side, slide the rolled portion of the diaper as far under her as you can get it. Then turn her on her other side and pull it through. Straighten it out and fasten it.
Hopefully, you have a hospital bed for her. If not then get one because if she can barely stand and is incontinent you are going to need it. Changing her diapers and bathing her in a hospital bed is a thousand times easier and safer than trying this in a regular bed because you can raise it to working level for you, and there's side rails for her to hold on to.

Beatty: "Sorry to stray from the topic... but I'm with Ann.. maybe it's time to stand back a bit & ask yourself some why questions.

It seems the goal was for Mom to stay in her own home, with her dog as long as possible? She cannot move to your home because the dog is anti-social? So you have kind of left your own home, spouse & pets for the dog's convenience?"

EXCELLENT questions!!! WHY are you doing this????

You brought back memories, and not in a good way 🤔
Try having her sit on the toilet before you tear off the depends, then have her stand again while you slip them off.
The inability to stand can be a real game changer as far as caring for someone at home, it is crucial in making safe transfers even when they can no longer walk. Ask about getting her some PT, I was surprised at how much some very simple exercises helped my mom (at least for a little while).

Either clean up in bed, lots of sit & stands from commode/toilet or a good dowsing with a hand heldhose shower attachment.

Sorry to stray from the topic... but I'm with Ann.. maybe it's time to stand back a bit & ask yourself some why questions.

It seems the goal was for Mom to stay in her own home, with her dog as long as possible? She cannot move to your home because the dog is anti-social? So you have kind of left your own home, spouse & pets for the dog's convenience?

Could you fence off part of your yard for it instead?

What is the plan for the dog when your Mom's needs outweigh home living?

Best to change her when she is in bed. Needless to say, wear rubber gloves and use a large disposable pad made for this purpose. Have two wash rags and two containers of warm water. It is a messy job no matter how you manage it, but this way the mess is contained and predictable. Having her stand in front of the commode would be ideal but is not, as you have found, the neatest way to accomplish a change. I share this from experience. Good luck and think about yourself! Too often, we get lost in the infirm person’s needs and forget ourselves. That becomes a lose/lose if we are not careful about considering our own frailties and humanness!

Is it time to ask yourself how long you “physically/mentally can” take care of someone in your mother’s condition, since you’ve left the comfort and peace of your home to spend part of your day cleaning feces from your mother and the facilities that she uses.

How is this “messy and stressful” for your mother?

Sometimes when we are caring for someone, “caring for her at home” becomes a goal that progressively becomes more and more difficult without us as caregivers realizing it.

Cleaning up after an occasional bathroom problem, or losing a few nights’ sleep, or having to “visit” in your OWN home can be a difficult and frankly exhausting and self defeating set of circumstances even when they’re temporary, but as a lifestyle?

Do you miss your husband? Doesn’t he miss you? Is it time to reflect on what you physically/mentally CAN do and consider what instead, you SHOULD do, to balance out what your present situation is offering your mom, your husband, and most important, you?

I’d never mention this if I wasn’t speaking from my own experience. I understand where you are. Hoping you are taking very good care of yourself.