Hopefully you also have a Realtor, but if not, you may need an attorney at this point. If the same Realtor is representing you and the seller, then you should insist on speaking with the managing Broker of the agency, and if you are still not satisfied, call a good attorney.
Does Fannie Mae actually own the house, or is this a pre-foreclosure? If it is indeed Fannie Mae, then you need legal advice about how to proceed. You may have to use a Fannie Mae approved contractor if you are using a Fannie Mae mortgage because they want to be sure that the work is completed appropriately to retain the value of the home they are loaning you money to buy. At the very least, you should be able to get a couple of quotes from several different contractors approved by Fannie Mae. I will be very curious to find out what happens. Please let us know.
Get your agent on this! I'm assuming the reason you are getting this work done during escrow is because you can't close your loan without the repairs? There is NO reason why you should put any money into a home that doesn't belong to you yet, it's a risk. If the repairs must be done prior to the close, then have the seller pay for it and you can reimburse them at the close, or have the money come from escrow. But if the deal falls through, make sure they don't charge you....you are not obligated to fix up a home for the bank.
If they are requiring you to pay at all....insist that you pick the contractor.
Your agent should play hardball.....force the issue!!! They want the deal!