SAHM with dog problems PT 3

Yes the dog gets played with. We don't have her tied up bored all day. Like I said in previous posts, we have a 4 year old daughter and she is constantly running around and playing with the dog. Both of them waste their energy together... Expect when the dog randomly shits inside the house then that's when she gets time out and tied up by the back door. When we would leave and leave her in her crate, we left her toys inside with her but she never played with them. She doesn't like toys. She currently has 3 and she hates them. A squeaky monkey one, a ball, and a bone snapped chew toy. She has also gets bones to chew at least twice a week. Those keep her entertained but that still doesn't solve the pooping problem. 
Also, I mentioned we live in a townhouse, it's a 2 story home. She's always running up and down the strairs but since I don't like her being upstairs bc I'm afraid she's going to poop all over the upstairs carpet (which has already happened 3 times), she's mostly downstairs. I also said we have a cat, and both of them chase each other around as well. She's a pretty active dog. And when my husband comes home from work he sometimes plays with her. Her last walk is around 11pm and that's when we go all go to sleep. 
++++++++
I just walked her around 3:15pm and I was outside for literally 20 minutes bc she wouldn't poop. Now she's currently tied up outside and she took a dump by the back door. 😒