When I was taking my driving lessons, my instructor gave me some advice which I believe still holds true: "Don't worry about the guy behind you at a junction. Ignore the fact that he's creeping onto your bumper. Take no notice when he sounds his horn. Disregard his looks of frustration and two-fingered signs. If you're not 100% sure that it's safe to proceed, stay where you are". It seems unfortunate that your instructor didn't offer the same advice.
Like others, I agree that the accident was your fault. Driving without due care and attention can result in anywhere between 3 and 9 points. (It can also result in immediate disqualification, but I think that's very unlikely). If you acquire 6 points within the first 2 years of passing your test, your licence will be revoked. (That's mandatory; the court and the DVLA have no discretion in the matter).
So your aim must be to keep the number of points on your licence to fewer than 6. Here, at least, you're in a favourable position (as far as retaining your licence is concerned). Magistrates are told to only consider 'special circumstances' in exceptional cases. For example, they're told that they should not take into account a possible loss of employment if someone loses their licence. However, if a 'third party' (in this case, your daughter) might suffer, they can consider 'special circumstances'. You should plead guilty and engage the services of a solicitor to plead your case for a penalty of fewer than 6 points. If you can keep the endorsement down to 3 or 4 points, you're probably also looking at a fine of around �250, costs of around �60 and a �15 payment to the victim compensation scheme. (However, fines are based, in part, on the ability to pay. Some are much lower than I've suggested. A few are higher)
Chris
PS: I hope that your daughter makes a swift and full recovery.