I agree w/Saspotato...while the noseclip idea could be of great help, it is possible your wife might become dependent upon them and that wouldn't be good. Here is what I would start with: have your wife sit on the steps of the pool with a snorkel only. Have her lean forward to put her face in the water and practice breathing in and out of the snorkel keeping her face (doesn't have to be her whole head) completely submerged. She doesn't have to open her eyes for this! She should recognize that this is a low-stress situation in which she can easily help herself if she becomes panicky or overwhelmed and snorts water.
Once she becomes comfortable with this, I would progress by having her sit further down on the steps and put her whole head under water and repeat the same process. Again, no mask, only snorkel. After she demonstrates a solid comfort level, I would then introduce the mask and repeat the entire two-step process all over again.
I know some people might think this is redundant but I've seen people do just fine underwater w/o a mask and their whole face surrounded by water - never snorting even a drop of water - but when they put the mask on and water gets inside, they freak out. So trying this two-step (face partially submerged, then entirely submerged) method in two separate phases (with snorkel only then with mask and snorkel) eases the person into feeling comfortable with their face completely surrounded by water and also feeling comfortable
with water trapped against their face inside the mask - another sensation altogether!
Good luck and hope this info helps! I had very similar issues when I first started out but with time and practice, I overcame it and now I teach scuba!