If you are asking a forum of lawyers whether you should get a lawyer, you might not be surprised that most would reply in the affirmative.
If they aren't going to pay for the damages, your choices are to sue them in jp court yourself or hire a lawyer. The first is probably cheaper, but the second is more likely to get it settled.
This is not legal advice. You should always discuss the specifics of your issue in person with an attorney. Be aware that there are time limits on all claims that depend on the kind of claim, so do not delay in seeking an attorney.
When you say "liability claim," I must assume you are talking about damages other than to your vehicle (i.e., the pole). If you told the insurance company the same story you told us in this forum, then I am not surprised they are investigating. Your liability coverage follows the vehicle only for drivers who are operating the vehicle with your consent or permission. It sounds like your daughter was operating the vehicle without your permission. Likewise, your insurance company might deny coverage for the liability claim.
As for the damages to your own vehicle, that should be covered under your collision coverage (if you had it).
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