Hi, the kids, just like you, are permanent residents and not K-1 / K-2 anymore as far as I can tell from your message.
When it comes to visas for Bahamas, this is what I found:
"For visits NOT exceeding 30 days:
An original Alien Registration Card (Green Card)
A national passport (passport from country of birth), valid for at least six months at the time of entry"
I'd still confirm with cruise line whether visa is needed or not. If you're not entering Bahamas, I don't see the need for visa, but this is not an immigration advice.
As for your discrepancy between name in passport and on GC, carry certified copy of marriage certificate.