At the border, renewal can be done any time before expiry with a new letter, ideally weeks ahead. A USCIS extension should be filed before the current period ends; she may keep working for the same employer for up to 240 days while a timely extension is pending.
File before expiry, and choose the route that fits the calendar
There are two ways to renew. The first is to leave the United States and reapply at a port of entry with a new employer letter, which produces a new three-year admission on the spot; the new period runs from the date of readmission, so applying a few weeks before expiry costs little time and avoids a gap. The second is for the employer to file Form I-129 with USCIS before the current admission expires; a timely-filed extension for the same employer allows continued employment for up to 240 days beyond the expiry while the case is pending, and premium processing can shorten the wait to the published window.
The health-care certification and the state licence should be renewed well ahead of the immigration renewal, because an expired certification stops the admission. A change of employer must be handled before she starts the new job, and the sixty-day grace period after employment ends is for departure or change of status, not for working.