Car accident both insurances disputing liability

Hello everyone,

I would highly appreciate your advise on this matter.
I had a car incident last November at the Dublin airport roundabout.

I was coming from Swords proceeding towards Santry, the third part from the M1 going to the airport.

I passed with a green light, the third party was apparently in a hurry and passed with a red light, a taxi driver stopped and told the lady she passed with a red light.

The right side of her car hit the left front corner of my bumper and left wing, left wheel was touched too.

Gards have not been called at the scene, the lady asked me not to call as she was in a hurry (relative had to catch a flight)

I agreed, she confirmed she was at fault, I have a recorded video where she confirms this, we exchange details and several texts she sent me where she wanted to pay privately for my damages...I have notified my insurance policy and filed a report with the airport garda station.

We didn t go anywhere with the private quote so I engaged the insurance company and so did she.

In the end it seems both insurances are disputing the liability, this happened around the beginning of February.
I have forwarded to my insurance company all the documents I have, taxi driver reg, videos and text messages I have, but nobody moves a finger.
My car is driveable but needs tracking...

What is it going to happen next? My insurance cannot give me a clear answer.

Also, what if I buy a new car? will I get a cheque for my damages if they rule out she was at fault ( which she was of course)

lastly, shall I seek legal advise? It would be such an injustice if they rule it out in her favour ...

Thank you all in advance and apologies for the long post.

Thanks,

R.