MCL 500.3177 applies to insurers not insureds. As an individual, you cannot petition the SOS to suspend the other person's driver's license.
Your insurance company will seek a judgment for any monies that they pay out.
Your insurance company will not provide you with an attorney to recover uncompensated damage to your car. They will only go after what they paid out.
You can still sue her. You will likely win by default because she probably will not answer the complaint. However, the practical reality is that you will spend a couple hundred dollars in court fees and will likely never collect a dime from her.
These are some of the worst situations because you did everything you were supposed to do and this other person did not yet it feels like she will "get away" with not following the rules. I wish I had information for you that is more favorable.
This brings up a great issue... in order to protect yourself in the future, make sure you have adequate Uninsured and Underinsured Motorist Coverage (normally described as UM/UIM COVERAGE). This extra coverage is not part of the basic plan sold by most insurance agents. This coverage protects you in the event an uninsured (just like this woman) or underinsured (someone who only has minimal coverage) crashes into you and causes you or your family serious injuries. The coverage is inexpensive and critical to have in Michigan. Current statistics show 1 in 3 cars on the road in the Detroit area are uninsured. Read more about UM/UIM here on my website: http://www.michiganautolaw.com/no-fault/uninsured-motorist-coverage/index.php
I wish you the best.
Please see the Michigan Secretary of State's website, concerning rights of injured parties in uninsured auto accidents: http://www.michigan.gov/sos/0,4670,7-127-1627_8665_9078-27180--,00.html