First, congratulations and we are thankful the daughter is fine.

The inspector made his statement out of typical bureaucratic overkill. If he knows there is a problem there he has to take drastic action to justify his existence. Remember, the more control we give govt, the more they grind us under the heel. Don't involve them if you can avoid it.

The peeling door jambs and trim can be pried off with minimal disturbance, cut with a utility knife along the edge with the wall to prevent tearing. Cut to proper length outside and dispose of into a box or trash bag and set on the curb, spreading this out over several pickups so the trash guy doesn't complain. Install new jambs and trim with safer coatings.

Paint over the walls. As long as the lead is not disturbed, it is not a health issue.