Can I open two claims on separate insurance policies?

In April, a cement truck’s brakes failed and slammed into my car, ultimately deeming it a total loss. There were no injuries and I wasn’t in the car at the time. I don’t know if the driver suffered injuries as they left the scene but I was able to get in touch with the owner who admitted fault (on behalf of the driver and the company) and said as much in an email.
I was advised, through friends and family, to go through my insurance company (company #1) and file a claim and let them subrogate the cost of damages to the cement company’s insurance (company#2).
I felt this was wise counsel and my company determined I was not at fault; however, once my insurance company offered a settlement less $6k for the car’s ACV, I thought perhaps I should’ve gone through the cement company’s insurance instead because they “should” have higher coverage limits. My car was less than 2 years old, bought new, with 21,000 miles.
I do not have gap coverage, but I paid a large down payment on the car thinking that would absolve me as much, clearly I was wrong.

I have yet to accept my insurance company’s settlement offer. What I want to know is:

1. Can I open another claim for the same accident on the cement company’s insurance (company #2) ?
2. Is this considered double dipping if I haven’t accepted a settlement yet?
3. Should I open the claim with company #2 and close the claim on company #1?

Lastly, if I accept #1’s offer, I’m confused about how to go about filing a claim of diminished value with #2?
I’m under the impression that if I accept any settlement offer that precludes me from going for another claim against #2.

I live in California. Any helpful advice is appreciated.