You have secured work outside the US. That and your suggested travel pattern for your spouse will raise red flags. Not advisable.
She should apply for the reentry permit. She can request it to be sent to the HCM consulate for pick up but she must not leave the US until
1. she has the notice of action for the application
AND
2. she has either completed the required biometrics or has bern notified that biometrics on file have been reused.
This will give her 2 years from the date if issue of the permit when she can reenter the US without being presumed to have abandoned her LPR status