As a custodial parent, it's partially your job to foster a good relationship between your child and your ex-spouse -- even if you can't stand your ex.
Believe it or not, the court expects custodial parents to go out of their way to make it possible for non-custodial parents to have a good relationship with their children. If you don't make the effort, you could end up finding yourself on the losing end of a custody battle.
How can you do it? Follow this guide on helping your children connect with their other parent:
1. Don't worry about what your ex does
Don't get hung up on your ex-spouse's failings as a partner, a parent and a human being. Focus only on what you can do to foster a good relationship between your ex and the children -- not on what your ex does (or doesn't) do. Just keep good records so that you can show the efforts you've made if you're ever questioned.
2. Be civil to (and about) your ex
Never denigrate your ex in front of the kids and always keep your tone polite when you have to communicate with your ex. Think of your relationship at this point as a business -- raising kids -- and conduct yourself accordingly. If possible, occasionally praise your ex to the kids. Even if your ex isn't civil, you'll have no reason to regret your words in court.
3. Honor the visitation schedule in all ways
Make sure that your children are always ready to go for visitation and encourage them to enjoy themselves. You don't want them to feel guilty for being away from you. That could end up making them reluctant to be around either of you in response.
4. Stay focused on the children
Remind yourself that you aren't doing this for your ex's sake -- you're doing it so that your children grow up into healthy, happy adults.
If you do have an issue with your parental rights and responsibilities that seems difficult to handle, an attorney can often help you sort through your options and guide you to a solution.