Hi Anna, welcome to Splitcoast!
Glossy cardstock is a slick surface so your dye-based inks (like Distress) are not going to work on there. Alcohol shifts alcohol so the normal go-to ink for a glossy surface (Stazon) is not going to measure up either since it will just lift your background colours.
I would try Brilliance - it's pigment ink and won't interfere with the alcohol and providing you leave it alone for long enough (or gently heat set it) it will dry on pretty much anything.
Make sure your alcohol ink background is thoroughly dry to give you the best chance of getting a clean impression.