Auto Insurance Claims: a driver hit our house, accurate answer, homeowners insurance

Question
A lady ran into our house 8 days ago here in Texas.  We contacted our homeowners insurance and her insurance right away and agents came out the next day.  We have been trying to get her auto isurance to pay but they are giving us the brush off saying to use our insurance because it will be faster and they have to wait for medical records of the driver to see if they are liable (who went to the hospital and police report said was under the influence of drugs).  Our insurance did an estimate, which was much lower than the estimate of the contractor we used and our insurance also said they sent us a check today for their lower amount even though we told them to hold off to see what might happen.  What are our options at this point because we ultimately want her to pay but just want our house fixed?  Will we be able to get more money even if we cash that check to get started with our contractor, or are we basically agreeing to that amount if we cash it?  We don't know what to do!

Answer
Hi Amanda,
In order for me to provide a more accurate answer I would like
some additional information.  You can change your reply to
PRIVATE if you so wish.

What was the dollar amount estimate from your contractor?

What was the dollar amount estimate from your insurance company?

Do you carry a Home Replacement Cost Endorsement on your policy?

Bennie
San Francisco Bay Area