Advice on pursuing claim week after, pls help

Please, i hope i can get any kind of input. A week ago a driver hit me, completely their fault. We were waiting at a light which has 2 right-turn only lanes. The other driver was in the right most lane southeast of my car. When the light turned green i started my turn, following very clearly marked lines on the ground (and a lot of signage stating its a turn lane), and the other driver tried to drive straight, hitting me in the rear right side. (i guess i could add there was another car slightly in front of me, that cut me off to go straight, i believe the person who hit me was trying to follow that car, they may even have known them). the damage wasn't too bad considering it was low speed but there is a significant dent and scratches.

Anyway we exchanged information and the other driver was apologetic. I get home and filed a claim with my insurance. My father suddenly (who i live with) decided i should try settling outside insurance with them, fearing my records or premiums and such will also be effected in some way. (I'm aware its against the law to raise premiums if I am not at fault but I'm not sure, he was worried about a lot of things). I called my insurance and said i would wait on moving forward. The other driver and I discussed getting an estimate and settling on some amount after. the estimate i got from the shop is quite large (roughly 5k). I understood they wouldn't want to pay the complete amount, but i would have settled with half or even quarter of the amount. to put it shortly, now the driver said I'm lying about the damages, doesnt believe my car had a dent, that i was taking advantage of them and extorting them. they offered 500. I told them i could still go through their insurance since they couldn't pay a satisfactory amount, and the other driver said they would lie and say I had to pay for their damages too.

I understand the mistake of listening to my father. but now Im not sure what to do. The current situation now is I have claim number with my insurance that is closed (i forgot im liability only and they deemed i was not liable). I also have the claim number of my case with their insurance since my agent sent my claim to them. Im being told its not worth pursuing anything since the other insurance won't believe me if i just report on my own, no video or audio footage, only photos of the damage. I dont have much experience with this, I really don't know what to do. I'm really lost and stressing a lot.