Did the Duke Royar previously cheated on his wife? I don't know if I remember this right

I don't think he did. Duchess Roygar was suspicious because that other lady was competent in ways she could never help his husband as, so she felt lesser than her. But a few characters assured her nothing of the sort ever happened, so...
If anything, whatever duke Roygar interactions showed to his wife he was always affectionate and caring. So this might be just my opinion, but among all the bad things he could have been, I don't feel a cheater was one of them.