FIrst of all check your house insurance to see if there is legal cover for this situation.
If so persue with them, if not then you need to speak to the cars insurance firm and state that there were severe injuries and you will be making a claim. YOu will need a solicitor, its up to you what sort you go with - can be no win no fee or can be straight forward paid for by you. You need a personal injury lawyer.
Whichever sort you go for THE OTHERSIDE should be paying for it albeit eventually. SO when the claim is put together you include legal costs for the other side to pay as you should not be out of pocket as you did nothing wrong.
In the mean time keep every receipt as a result of the injuries - so car parking, pain medication, time off work, tutors if needed at home and so on and so forth. Set yourself up a file and log everything. Work with your daughter to document her side of the story, get contact details of any witnesses, any well known to you ask them for a statement in their own words. Get a police report if you can, get details of what they are pursuing other driver for and keep it all together logically. All of this will help in the long run with the claim.
The claim will have compensation for injuries, out of pocket expenses, legal expenses and possibly also trauma/mental impact so you need to think about all elements. For injuries there is usually a standard amount they will go for. They (lawyers and judges) often like everything to be done and dusted and recovered from before putting a final claim through (ie so signed back to health) but in longer and bigger cases they will do interim payments - this is a good sign as it means the other side admits liability and they are just quibbling about totals.
Get an appointment with a PI lawyer and go through whats what with them, get a cost from them and an idea of the total legal fees involved. ANy payout should be kept for your daughter and used for her benefit (you would effectively be her trustees for the amount so you might want to think about what the money should be used for/how it should be managed etc. A couple of grand is less onerous than say 50k. But you would be suprised how things add up