I need advice on how to proceed in an awkward fender-bender situation.

So, here's a long-winded story about a tiny fender bender I got into while driving someone else's truck (in California). I'm just not certain what my legal obligations are or how to proceed as it's proving to be annoying.

Jen = the owner of the truck I was driving Mandy = the owner of the car I hit

My wife was assisting someone named Jen for the day. This consisted of my wife driving Jen's big stupid box truck (like the smaller end of U-Haul trucks) all over the city, making returns. I came with her for company and to help out as some muscle. We dropped our car off at Jen's place and my wife drove the box truck away with only me as a passenger. After making a few returns, we had discussed that I hadn't actually added her to my insurance policy since we got married only recently. We weren't yet aware that my auto policy automatically extended to my spouse. To be on the safe side, we swapped and I drove Jen's truck because we knew for certain I was insured in case anything happened.

A few more returns down the road, I parked Jen's truck on a street that had several parallel parking spots on either side. I parked in the 2nd to last spot on the right before an intersection. There were zero other cars parked on my side of the road, it was completely empty other than the truck. We made the return and came back to the truck and still no one was parked behind me (I know because I put something in the back of the truck). However, someone had parked right in front of me, quite close to my front bumper. This wasn't a big deal since there were no cars behind me, I had all the room in the world to reverse.

We got in the truck, started it, and I thoroughly checked my mirrors before backing up. Then, as I backed straight up, I hit something. I immediately stopped and pulled forward a bit, thinking I somehow clipped a parking meter or tree branch, but otherwise I was absolutely confused because no one was behind me as I had -JUST- checked in every possible way I could. Turns out, someone by the name Mandy had JUST driven up -through- the parking spots, entirely in my blind spot and parked right on my ass to read her phone while I was checking my mirrors and beginning to back up. Her tiny, Japanese, hybrid car was invisible to me without getting out of the truck because of how closely she unnecessarily pulled up behind me.

The damage to Mandy's car was a minor scrape/line across her front bumper and there was no damage on Jen's truck. There were zero injuries whatsoever and Mandy admitted to having just pulled up and being on her phone, blah blah blah. We exchanged information but I had no information on Jen's insurance, or if she even had any. All I could do was supply Mandy with all my information and Jen's name and the license plate of her truck. Either way, I assumed I was entirely responsible and was willing to take the hit to my insurance. However, California states that the primary insurance is the policy on the vehicle while the driver's (my) insurance would step in as secondary if the primary policy didn't cover the total losses.

After going our separate ways, and upon informing Jen... despite there being zero damage on her truck, she was extremely upset. She did not want to involve her insurance whatsoever because she expected to be dropped the moment she had another incident with her truck (I'm assuming her accident/driving record is awful). Mandy made her claim with her insurance company, and I decided to make the same claim with my insurance to make sure they would communicate and get this done and over with as soon as possible. However, neither insurance company can move forward whatsoever with the claim until they find out about Jen's insurance policy on the truck.

Here's where it's getting sticky. Jen is refusing to share her insurance information despite it being her vehicle. She doesn't want her insurance company to know about this incident. Jen is absolutely insisting I settle privately but Mandy is very uninterested in dealing outside of her insurance nor would it be affordable for me to pay out-of-pocket to whatever Mandy's mechanic/insurance thinks fixing this bumper will cost... not including any inconveniences like a rental car or what-have-you. It's tempting to throw my hands up and hand over Jen's contact information to Mandy's insurance company but the tricky thing is that we want to maintain a healthy relationship between Jen and my wife, as she works freelance for Jen.

Is there any way to deal with this in California with completely cutting Jen out of the process? Mandy's insurance probably doesn't care who takes responsibility, but after speaking to my insurance, they would simply deny the claim outright if they don't get enough information about all of the involved vehicles' policies. Jen just seems to think that it's one's right to settle privately and is trying to force us to do just that so we can avoid involving her. Is it even possible at this point since Mandy has made her claim? I just don't know what to do that wouldn't bankrupt me or piss Jen off and cost my wife her job. I have a feeling that it's out of my hands at this point and she is breaking the law by refusing to be involved...

My gut says that Jen should just suck it up, give her information, but insist that I was not given permission to drive the truck and that only my wife was, so she won't be held liable. It sounds like the best bet, but Jen is being difficult about even mentioning it to her insurance whatsoever. Is the only way to give Jen what she wants is to have HER settle privately with Mandy's insurance?

Any input would be appreciated!