My cat keeps pooping on the floor

[K_T]

My female cat has made a habit of pooping on the floor.

She is a tortoise cat. She is about 4 years old and is a few ounces shy of 20lbs. She is the "second" cat of the house. The cat that was here before her is a black&white male cat that is about the same age (maybe two weeks between them) and is about 14lbs. Both of them are strictly indoor cats.

She has always been very friendly and rather smart. She had some surgery done to remove a cat toy she had eaten, and she got a little meaner to the male cat. (She used to be a pushover when it came to him bullying her, but now she doesn't put up with anything.)

She is not very smart when it comes to using the litterbox, somehow. She all but sits down in it when she poops, so it clumps around her butt. She is obese, so she doesn't seem to bother with cleaning it off herself. It can get bad enough that she can't go anymore and she begins to vomit. Because of this, we clean her ourselves about once a week.

She hasn't always done this, either. She only started about a year ago.

The litterbox is and always has been located at the back of the garage and is easily accessible. It is very large and we have tried using both the clumping litter and the thicker kind for scooping.

There are some cats that hang around the garage door, and after reading up on it, I thought it might be because of them. They don't frequent that place much anymore, so I don't think it could be because of them anymore.

She almost always poops on the garage floor, though quite a ways away from the litterbox most of the time. (It's only almost every other day that she doesn't use the litterbox for this, but it's becoming more and more common now.) She pees in the litterbox just fine, though. She has even used the litterbox to pee and then got right back out of it to poop on the floor right in front of us.

We have tried scolding her immediately when it happens, using either a strong and upset tone of voice, spanking her (not my idea), or simply placing her back in the litterbox when it happens.

She doesn't seem to get the message that we're not going to tolerate this, even though she seems to know what she did wrong if we discover it hours after she'd done it. (She always runs and hides in fear when she hears us find it.) My mom is actually considering having her put down if she doesn't stop.

The last thing I can think of at this point is a diet problem, or some kind of thinking pattern that leads her to this. (Maybe for her, pooping in the litterbox means getting the litter clumped around her butt, which means either vomiting or unpleasant cleaning, so she thinks just not pooping in the litterbox will solve the problem?) Like, maybe if she were thinner, she could clean herself and it wouldn't be leading to something unpleasant.

I know she's obese, and I've been telling my mom that we should cut back on her food and put her on a serious diet ever since she started becoming too much to hold comfortably. My mom, not exactly a healthy weight either, has been in denial the past few years and has been unable to say "no" when the cat begs for treats (specifically shrimp), and has even switched them over entirely to the Friskies Party Mix rather than normal dry food. I myself know this is a horrible thing to do, but she won't listen to reason, insisting that they refuse to eat anything else.

I finally got her to agree to start them on a diet just today, but it's still not particularly healthy. It's the same party mix (but no additional treats), only put down every 6 hours. (6am-7am, noon-1pm, 6pm-7pm, midnight-1am) I have repeatedly suggested switching to something healthier, but she is totally adamant about them definitely refusing to eat anything else, and other lame excuses such as "if they're going to be miserable, they might as well eat something they like." She won't even take her to the vet to make sure this diet is alright!

I'll be taking over feeding them from now on, and I'll be trying to sneak a healthier food little by little to make her see that they will eat other things.

But this post isn't quite about me putting her on a diet. After she just pooped on the floor again today, I'm worried about what's going to happen if the diet doesn't work. What if even after she loses weight, she continues to poop on the floor? What else can I try to discourage her from pooping on the floor?

I'm hoping the people on this forum can help me. I really don't want to lose my cat over this.