Everyone makes mistakes and deserve a second chance. If she makes you so happy and you feel comfortable and happy with each other why not enjoy the moment instead of living in the past and letting it ruin what present and future happiness that you could have with her?
Yes. Nobody can ever predict what's going to happen in the future, and from your post you seem to be happy now, give and focus on this relationship with the 100% effort it needs to succeed instead anchoring yourself to the past.
Best of Luck!