Echoing @Procrustus - if your wife is suffering, get her treatment, she comes first, whatever your choices about the car. And of course, you both have my sympathy and best wishes.
Answering specific questions - In my experience (which is likely jaundiced), adding a lawyer for the Physical Damage side does very little if anything, and often increases your costs.
[ again, huge fudge factor for state laws, carrier differences, out-and-out shady companies, etc. ]
Most states have pretty boilerplate agreements making sure vehicle damage offerings are reasonably fair, not generous, oh hell no, but fair in the sense that a good adjuster in a total loss is going to show you how they got the vehicle’s final value (comps, salvage value, cost to repair, and any extra value like your new battery) and why it’s a total.
Absent shennanigans, a lawyer is going to charge you a few hundred to a thousand dollars to confirm it’s “customary and usual” for your state/market.
It’s your injury/PTSD claims where, exactly as Procustus said you may want to get a lawyer, but it’s likely NOT going to change anything about your vehicular damages claim.
Now, being extra clear, I didn’t handle injury claims. Way too much stress. But I still have a good bit of secondary info. In general (that word again) if you involve a lawyer, it shuts your conversation with the other carrier down completely. All communication will need to go through the lawyer, which may slow the repairs/settlement a bit. The Lawyer would want all communications to go through them for your protection.
The injury and expenses of treatment from your wife will most commonly go through your own coverage, both auto (MEDpay and/or PIP) first, then your own health coverage, and when complete, the carrier will subrogate their costs against the other company, and your lawyer will attempt to recover any of your out-of-pocket costs from them as well (co-pays, co-insurance, etc.). Which is helpful, but depending on the fees charged for the service, may not make a difference in final costs or quality of care.
Where the lawyer will be very helpful, is if you make a claim for pain and suffering against the other carrier. Whic his probably the only thing that is going to get you additional money, rather than just the typical insurance dodge of “making you whole”.
If you DID get a settlement for pain and suffering (or court judgement) you could choose to use some of it for additional car repairs, but that likely wouldn’t happen until after your wife’s treatment is complete, all the lawyers (on both sides) argue over the treatment, the degree of suffering, and settle in or out of court.
IE you should at least consult with a lawyer because of the pain your wife is going through, but in terms of getting your car fixed, it’s going to almost certainly be moot either way.
Again, I’m jaundiced, in this thread or one of the others, I had many a claim where I handled it in good faith (non-injury, note), a lawyer got involved, and I was forced to stop everything. Adding in a few months, nothing would happen, and either the legal team would take over, or 4-6 months later I’d get a letter saying the lawyer had withdrawn (no money) and a sheepish person would say they ended up paying a few grand to a lawyer who said everything was normal.
But that was reeeeaaaaaaaallly rare, most of the time I didn’t get a formal letter of representation, but a client might say they talked it over with a friend/family attorney to tell you the same sort of things I just related - not much to work with unless it’s an injury, and even then, it only changed the injury/pain and suffering part of the claim.