Even if your spouse wasn't a good marital partner, that doesn't necessarily mean he or she isn't a good parent. Not recognizing a partner's parenting contribution to a family, or capacity to be a nurturing caretaker, is one of the biggest roadblocks in resolving custody issues.
Your spouse's style of parenting and values may be different from yours. However, that doesn't mean they're necessarily wrong or bad. If you want the best possible outcome from negotiations with your spouse you will have to extend some tolerance. Divorce is not a perfect situation, and options and resources are limited. What's best for your kids is two parents who can get along agreeably in raising them, while leading separate lives. To accomplish that you'll need to be flexible.
McAdams Law represented a husband in a custody case who began to exhibit sexual preferences and a lifestyle his wife found repulsive. She attempted to force him out of his children's lives through Court proceedings. The matter was successfully resolved for this client by negotiating an agreement with his wife wherein he kept his sexual practices away from his children. This calmed her down, and allowed her to see that his involvement as a father was important to the well-being of their children.
The moral of the story is: differences in opinions, values or lifestyle aren't sufficient justification to end or severely limit a parent's participation in the lives of children. Unless there is reason to believe that your kids are genuinely in danger, look to build bridges of cooperation, rather than to burn them.