She studied at Cardiff University where she met Neil Kinnock. They married and had two children. Glenys felt that it was important to be with her children rather than pursuing a political career. When they started school, she returned to teaching and was able to combine her work with looking after her children. She says that she doesn't have any regrets about her choice.

"When the children were growing up I was a teacher and I did tend to feel at that time that my husband's work as leader of the party was very time consuming. He was always very busy, worked very long hours, and I did feel the need to compensate for that and I don't regret for one moment the fact that I did that. I think if your children grow up into nice human beings that you're proud of, then that has to mean you've done something right and I feel that both parents being preoccupied with very time consuming careers was not really appropriate for us and not something I would have chosen."