Wife sprained (grade 2) ankle at a park, ER visit required. Insurance offered $250 settlement. Is this typical or low?

No — this is a lowball opening offer, and by a wide margin. A few reasons why:

• The treatment itself signals real injury. Ambulance transport plus an ER visit isn't something adjusters see for minor sprains — that combination alone tells a jury (and should tell an adjuster) this was a legitimate, acute injury, not a soft-tissue nuisance claim.
• A Grade 2 sprain is a partial ligament tear, not a mild strain. These typically take 4–8 weeks to heal properly and can leave lingering instability or chronic weakness if not fully rehabbed — which is relevant given PT was never completed.
• The claim isn't ripe. Your wife still has ongoing pain. Signing a "full and final release of all claims" now means giving up the right to any further recovery even if the ankle turns out to need surgery, develops chronic instability, or the pain simply doesn't resolve. Settling before you know the real endpoint of the injury is the single biggest risk in what's being asked of you here.
• The missed PT could be used against you — insurers sometimes argue a claimant "failed to mitigate damages" when treatment isn't completed. That's not fair given your circumstances, but it's worth documenting why PT didn't happen (housing situation, not lack of care) in writing now, while it's fresh, so that explanation is preserved.

Bottom line: insurers routinely open low with unrepresented claimants specifically because most people don't know the treatment and injury pattern here supports far more. $250 doesn't reasonably account for the ambulance, the ER visit, an ongoing partial ligament tear, or the fact that treatment isn't even finished.