Do not reissue tickets with a name that does not match her LPR card's name. If you do, be prepared for problems returning to the US. DHS knows her by the name on the LPR card. The LPR card name is the one with which she needs to exit and enter the USA.

An LPR only needs her LPR card to re-enter the USA, so if she manages to board the flight that leaves the USA, she will be fine upon return, especially if she presents only her LPR card to the CBP.

OP says the airline says they will board her if she brings her marriage certificate, so no problems there. I suggest when checking in for her return flight, she present just her LPR card and see if that flies. I've done that on flights from BLR on itins back to the US, and Lufthansa is fine with that.

The only issue would be if she presents anything other than her passport to a TSO. Unlike TSOron, some TSOs insist on a passport if the boarding pass is for a nonUSA destination. . Also see http://www.flyertalk.com/forum/check...tl-flight.html . Since she is an LPR, she should present her LPR card. If she gets push back, then she should present a copy of the CBP's web page that says that LPRs only need their LPR card to reenter the US. At the penultimate resort, present the passport and marriage certificate. Failing that, buy a refundable ticket in her passport name on a different airline, check in, present the BP, and cancel after clearing security.

Note that for travel back to the USA, the sole document an LPR must have is her LPR card. Thus it is not a mistake to have airline tickets that match the name on the LPR card; indeed it would be a mistake for the name on the card to not match the name on the airline ticket. If she were flying from a pre clearance airport outside the US, and the CBP officer asked for her boarding pass, then she might get a hassle.

The mistake was to have the name on the LPR card mismatch the name on the passport. After this trip, she should fix that by getting a new LPR card with a name that matches her passport. I never under stand why people insist on changing their legal name after getting married.

It is most fortunate that the child's birth certificate has both of your wife's names. That way she prove she is the child's mother, regardless what identification she uses.