Drunk Driver’s Insurance Telling Me To Claim Totaled Car On My Own Insurance?

My father was hit by a drunk driver in December in Richardson, Texas (DFW metroplex). The other driver was arrested at the scene, and my dad's car was totaled (thankfully he just had minor injuries).

The drunk driver's insurance policy only has about $25K collision coverage, but my dad's car was worth $32K at the time of the accident (with $17K left on the loan payment to Lexus). But the adjuster for the drunk driver's policy told us that we need to claim the car on our insurance, as the car is worth more than the loan payment remaining. I don't understand why we have to go through our insurance, when the other driver is at fault here?

The lawyer we hired for the case ended up being terrible. He didn't communicate any updates to us, including from the insurance adjusters, rental car company, etc. He abruptly ended the bodily harm settlement and won't provide any legal guidance for the car situation. What should my dad do? And what is the best way to hold the other driver's insurance company liable for the remaining costs of my dad's now totaled car?