What are my legal rights as a non-custodial parent?

Your ex is in violation of your custody order, and you must take him back to court immediately to enforce your rights. Don't use "self-help" by doing anything more than going to his house, knocking on the door and asking to take the kids on your days, because you'll put your kids in the middle of the conflict (even more than they already are) if he refuses to answer the door, or is hostile to you when he does answer. I assume you've already done this and if you do it again it will be futile. Don't let this go on any longer. You don't say how long it's been since you've seen your kids but this is hurting them even more than it's hurting you. Since you're the non-custodial parent I assume you're paying child support but if your ex continues to withhold the children from you, you could have your payments to him suspended until he complies with the order.