Get her a lesson. Teaching your significant other is a challenge because it sets up a power struggle in the relationship. Doing that will ruin a good relationship and make a bad relationship worse. I've seen it wreck tons of relationships. Better to get her some lessons or split the cost on an all women's program. Long term, you'll both be happier. Short term, at the end of the day you'll be able to sleep in the same bed that night.
I've been teaching snowboarding for 12 years, AASI Level III certified, and staff trainer at a mountain for 7years. Last season my gf wanted to learn how to snowboard and asked me to teach her and her friend and I refused. She was annoyed but got over it when she and her friend were in a lesson and saw a couple yelling at each other on the bunny slope. Now, the only teaching I give her are advice when she asks for it.
She's improving, we have fun riding together all day, and can still stand to look at each other at the bar after a day of riding.