According to CBP it is very important for her to have her green card.
Lawful Permanent Residents (LPR) of the U.S. must present a Permanent Resident Card ("Green Card", Form I-551), a Reentry Permit (if gone for more than 1 year), or a Returning Resident Visa (if gone for 2 years or more) to reenter the United States.
Since you're saying she has already boarded the plane, unless she is coming on a really long haul flight it might already be too late for courier.
The only option at this point I would think is to go to the airport and wait land side, communicate to her via email/text/Whatsapp etc to inform the CBP that she forgot her card at home and is available with her husband/someone else in the arrivals area. If they like they will be able to get to that.
They will not refuse entry before verifying different options they have to assess her residence status and the fact that her documentary proof is available with someone in the arrivals hall can only help, it can't hurt her chances.
What's still unknown is whether the card is close to Seattle airport or not. If the card also has to take a flight to reach there then unfortunately i think this question is being asked a little too late. She will have to attend the landing interview without her green card and try to convince them about it.
Do not courier it now, it is too late and it is far better to have it in someone's possession than to have it stuck in transit.
Since she has a valid visa which allowed her to board the plane, there are chances that she will be admitted under that status even if the green card can not get to her. In that case she will have to go to a deferred inspection site to get her admission status adjusted once she has the green card in her possession.
It is by a stroke of luck that this passenger was allowed to board in the first place. Future readers please note that this may not work for you the same way. On the US port of entry you may get away with it with just a scolding but the port of departure may flat out refuse boarding and that is a much bigger problem. So my advice would be to arrange for your documentation to reach you before your departure for US.