The very least you can do is to talk to your children about how they intend to show their appreciation for their father; and if they need help, you can give them a few sincere and thoughtful ideas. There are plenty of reasons why you'd want to do this:
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1. He is still the father of your children. Without him your children would not exist. A lot of women tell me they shouldn't have gotten married, but that's always closely followed by "but then I wouldn't have my kids." I have yet to hear someone say they wish they hadn't had their children.
2. He will always be the father of your children. Children should never have to choose one parent over the other. By talking to your children about Father's Day, you're showing them that they don't have to choose, nor do they have to hide their love for their father from you.
3. He shares the responsibility for parenting. As much as you and your ex may not see eye-to-eye on parenting, his perspective may help improve and strengthen your parenting. And when the going gets tough, any extra reinforcement of consequences and discipline helps.
4. He does activities with your kids that you don't. There are a lot of activities I'm willing to try, especially if my kids ask me, but there are a few I definitely won't … fishing, playing paint ball, and auto-maintenance, to name a few. I'm not wild about camping either. That's where my ex comes in, and he's happy to do "his" activities with the kids. That's a win-win all around.
5. His parenting time means more free time for you. This is a no-brainer. When your children are with their father it means alone time for you, doing whatever you choose or need to do. It makes life a little easier.
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More Father's Day advice from YourTango: