It sounds like you may be declared 'At Fault'. Your vehicle was the one moving at the time. Unless she was on a no parking zone or too close to the intersection.
If you inform your insurance, her insurer will also be involved and charge her an excess. It sounds like her excess is very high, otherwise, she would just put the claim in.
Turn the tables and threaten to call your insurer to do things legitimately, see what her reaction is. She may decide to cut her losses and go 50/50 with you.
You can inform your insurer but not actually put the claim in, they will only act on your behalf if you instruct them too. Also, if you think the other car was breaking any traffic laws, go to the police and get an incident number.