The term is called "demurrage" I think and you don't need to get it in writing first, it's just part of basic law. Basically any out of pocket expenses that this person has caused you, taxi, rental car of the same approx value of your own car are all acceptable.
Here's the thing though, you must pay for it up front, you must have receipts and you then send a letter of demand to the woman that hit you, she then passes it along to her insurer and they pay. Trust me, I've done this twice now.
Last time I did it I got a smarty at the other persons insurance company that said they wouldn't pay $99 a day for a rental car and I told her I was entitled to a rental car of similar type to my damaged car for the duration of repairs ($2800) and told her if she didn't pay it I would simply lodge the claim through the sheriff as an unpaid debt, they paid it 7 days later obviously after speaking to legals. The takeaway message here, 1) Claim what your owed 2) DONT be bullied by them!
The only downside is that you must pay for it first and you must send your claim for demurrage on a fairly standard "letter of demand" which you can probably download or ask your lawyer for a template.
I might even have one if you need it.