I'm the son of two parents who split when I was in grade school. My mother didn't handle it well. Once she had me taken to my church in order to get me to say bad things about my father. My dad wasn't able to see me for the first month or so but he'd sneak by to see me as I got off the bus from school.
Eventually, my dad got visiting and we ended up having me go to my mom's on Mondays and Wednesdays and my father's house on Tuesdays and Thursdays. I spent school weekday nights with my mother (both lived in town, but my mother lived closer to the school) and then traded weekends with either parent. My parents were also reasonable about trading weekends depending on if a family get together was happening. Holidays weren't difficult, as my mom's side of the family were early risers and my dad's side of the family were night owls. I'd do Christmas eve at one house, then the next day pop over to the other side of the family. I spent thanksgiving lunch with my mom, then would go to my dad's to have dinner with his side of the family.
The best part of the split was that, as time went on, everyone respected each other. My parents refused to talk bad about each other, especially my father: "You only get one mother, and she's yours. Just like mine was. Treat her with respect, she deserves it." It wasn't always this way, but people can act irrationally when it comes to their parents. I know that I've gotten heated just by someone trying to tell me my father was lazy.
It's easy to hate, it really is. Fight it. It'll be a battle every day. Especially with a child who is desperate to understand and you with who knows how many issues from the break up. Teach your kids to always respect their parents, don't try to turn them against your ex, and don't ever try to replace them with someone else. My parents are now both happy, doing their own thing. I spend time with each of them, as much as I can. I've shook the hand of a few people that either my mom or my dad have dated. It's still weird to this day, as I'm now living on my own in my late twenties. It's fine, though.