First off Welcome to the forum!
Others will have better suggestions for sure but I wanted to ask a few additional questions.
But before we start, with respect, dogs don't naturally know how to lie down or stay at a human's command. These things need to be taught so even though it's simple to you, your dog is not finding them simple....and this is NORMAL. Depending on how badly she may have been abused, this may also come into play...but it can be solved with patience good training and love in the vast majority of cases.
Please also know that most dogs want to please you and this sounds like a submissive dog. I say this because the peeing she is doing sounds like 'submissive urination'. Dogs do this to show you that they are submissive and it has nothing to do with housebreaking. Basically (if I understand this correctly) by peeing in this way (while being dragged) your dog is telling you that you are the superior and that your dog just wants to follow your lead. It's actually quite sad because the dog is trying to communicate with you in a delicate way, but we humans never see urination (even submissive urination) on the floor as delicate. We think it comes from a place of malice when it does not.
The problem is that you are not understanding each other.
1 - has the dog mastered sitting?
Meaning the dog sits every time you say sit. If the answer is no, imo that's the first command you should work on as it's a much easier one than 'lie down over there.' The dog needs to master each task before moving on to another task...especially harder tasks.
2 - How long have you had the dog?
That piece of info will be useful to other that I hope can help here.
3 - Would you consider obedience training (please say yes