Quite Overwhelmed

Wow.
I think you need to get your daughter evaluated. No offense. Lots of children will play or paint with their poo, but it's usually when they are much, much younger.
Is it possible she's angry that she isn't potty trained? Many times when kids start taking off their own diapers it's a sign they are ready to be done with them. Do you take her to the toilet on a regular basis whether she says she needs to go or not? And have her sit there? Do you take her when you go?
I had a 4 year old boy in my daycare that wasn't potty trained and I trained him. He took turns going to the bathroom just like the other kids and even if he didn't go, he took his turn sitting and then washed and dried his hands. We did that for about a week and he started using the toilet. I told his mom and she still brought him in a diaper every day and put a diaper on him before they left even though he'd used the toilet all day. He was 4. The first thing he did when he got to my house in the morning was take his diaper off and throw it in the garbage. I didn't do anything magic, he just did what the other kids did. They all took turns on the potty before going outside. They all took turns when they came back in, they all took turns before lunch and then after lunch. Everytime a kid said they had to go, I took him to take his turn too. I didn't ask him if he had to go, I didn't ask him if he wanted to, I just took him. One day his mom confronted me about none of the diapers she sent being used. He hadn't been in a diaper at my house for weeks.
My point is, your daughter is acting out for some reason. If you have babied her, that could be part of it. Maybe she doesn't want to be treated like a baby anymore. If I'm reading this correctly, she is progressing rapidly in her speech. Or, she's progressing rapidly with these other behaviors, I'm not sure exactly what you were expressing.
I know you have your hands full, but my first thought is to get rid of the diapers. At least during the day. Take her to the bathroom every 20 minutes and don't take your eyes off of her long enough for her to smear what comes out of her all over the house.
If she thinks poop is so fun, tell her she has to clean it. Anything she smears it on goes in the trash. Make her put it in the garbage. Keep toys in bins that she can't get her hands on.
Try some of these things and talk to the pediatrician. A 4 year old acting out with poop......by that age, kids know to watch where they're walking because they don't want dog poop on their shoes.
She might just be acting out, but you need to get to the bottom of it for sure.

Best wishes.

You need to have her evaluated. Call the school district and find out how to proceed. Also, join parents as teachers if you haven't already. I am usually not an advocate of too much intervention. I like for children to be treated very normally and mainstream. But your daughter has at the least emotional problems and at the most some sort of diagnosis that could go in most any direction. It concerns me greatly that she's doing this at her age. This is something that would normally be a 2 year old thing to do. With her delayed speech it's obvious that you could use some support.

I would make her (attempt to) clean it up! 4 is way too old to be doing something like this, and I know from experience (with my own kids) that 'fun' things suddenly lose their appeal when a person is made to be responsible for their own messes.

She will surely not do the best job and you will have to go back (when she is not looking) and re-do the cleaning, but DO make her do a decent clean up job first because she should not know you are coming after her.

Although she may be a delayed speaker, she isn't mentally challenged. The fact that she started spreading her poop around after you repremanded her, let's me know that she knows what's she's doing. Us as parents have to realize that we are in control here. Our children know more about mind games than we give them credit for. I know its hard for you with 4 young kids. Practice and persists pays off. Besides, pampers aren't cheap.

Have you had her tested for any mental delays or illnesses?

If it was a one time occurrence - I would not have mentioned the above, but sounds like it's happened at least a handful of times. I'd have her tested for a full spectrum of delays and mental disabilities.

.