It's not about the "present", and if you think it is, then you're a shallow asshole.
It's about giving a day to your wife and the mother of your children. Doting on her whenever possible. Breakfast in bed, cooked and served by the kids. Encouraging the kids to make her something special (you know, those clay "masterpieces" that she'll keep forever, tearfully pulling out in 20 years, saying, "remember when!"). Telling her she's the best mother of your children that you could hope to have (which you should do often, anyways, but especially today). Doing things as a family (go to the zoo, park or be a tourist in your town).
The reason that you, as a husband, should do something for your wife on Mother's Day, is because, a) she is the mother of your children, and b) there is no "Wife's Day".
Uber, I am interested, though. You said "I expect no present from the mother of my kids on Father's Day" then said "this is why I'm single." If you're single, why even bring up an expectation presents from your wife? Do you have kids and are divorced? If so, I don't think that anyone expects ex-spouses to give each other anything. Even the most amicable split ups aren't THAT amicable!