Too often, parents get into competitions over the kids, and that's usually not a good thing. If you want to be well-remembered as a parent, maybe you should consider treating the other parent nicer and doing what you can to encourage a close parent-child relationship with both parents.
1. Enable and encourage the kids to have regular contact with the other parent. In addition to personal visits, phone calls, texting or computer contacts, initiated by the kids would really be good.
2. Demonstrate a good relationship (if possible) with the other parent. At least be civil. Keep in mind that the kids understand they are part you and part the other parent. They may see you being mean to the other parent as you being mean to them.
3. Help kids learn to show their feelings for the other parent. Help them find gifts, buy or make cards, etc. Encourage the kids to spend some time with their other parent.
4. Help the kids to remember holidays, birthdays and family occasions with the other parent. Kids may not know what to do when they're young, so they need some guidance. When they are older, they may just not think about these events. You can help everyone by talking with your kids about the events and reminding them so they can participate.
Note: All this works equally well for both parents. Moms and Dads should work together to encourage the kids to look forward to various personal and family occasions. Father's Day is coming up, but helping kids stay in contact with both parents is a year-round job. Do your kids a favor and teach them good ways to stay in touch with their extended family.