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Hello! Thank you for bringing your question to JustAnswer! I'll be happy to provide some valuable information!
From the details you provided, it sounds like you would NOT be violating the agreement if he technically has to work on those days (I cannot say this for sure without seeing the agreement), however, you stated that the relationship is important to you.
Perhaps you can work out another arrangement that makes more sense to you (more vacation days perhaps), I strongly recommend you consult with an attorney or mediator in your jurisdiction to get in writing.
You might also want to consider that it sounds like for the most part, the child is with him most of the day. Most 11 year olds are asleep by 9pm or 10pm. If you think about it, dad is working during the child's sleeping hours. Even if he is being left with the step mom, for the most part he is sleeping during this time. (Just something to consider).
If you are not comfortable with that, perhaps you can ask Dad about his days off and work out a new schedule based on those days if it is feasible. With regard to your child, it's really up to dad whether he wants to do things with him other than hang out at home. Maybe you can suggest he do something fun with him. If your child feels strongly about it, you may want to offer to sit with a family therapist to discuss how your son is feeling and ways in which they could spend more quality time together.
Otherwise, you would have to go to court and argue the terms of the agreement no longer serve your child's best interests because Dad's days off are during the week and Dad is 100 miles away.