I have Progressive Insurance and they said that I have to pay the deductible on the damages and that it would go as a claim on my insurance and then after the work is done, then they would send the lady the bill and hopefully she would decide to pay it.
That doesnt sound right. Its almost like Progressive (my auto insurance) doesnt want me to do anything. Just go away and keep the damages.
And why should I have to file it as ANY type of claim on MY insurance. It should go on the ladies homeowners insurance right?
Yep. Standard practice. If they succeed in recovering from the third party you get your excess back.
If you think you'll succeed in getting the third party's insurance details and getting them to pay up, go for it. It's a lot harder to do that especially if they are denying liability ....