Change of status is also routinely denied after waiting a long time. Good that she doesn't want to do it.
File for adjustment of status to get GC after marriage.
Forms: I-130, I-130A, I-485, I-864, I-693, I-131 (optional, but recommended), I-765 (optional, but very recommended), G-1145 (optional).
Lawyer is optional, many do it DIY. But good representation never hurts.
Many months of wait, foreign spouse won't be able to work or leave the US for a while.