As Digby Jones would say - communicate, communicate, communicate!
DP and I talk about everything and always come to an agreement
This eliminates the risk that there is simmering resentment, and we are both trying to achieve the same thing.
I used to think that presenting 'a united front' would lead to the DSC resenting me, because DP was a bit of a Disney dad for a while. DSD does blame me for her Dad changing, but DSS recently admitted that 'dad' was definitely the strict one of the two of us, whereas I'm a bit of a softee! 
Seeking outside help/support from professionals has been key for us too - we have been on parenting workshops, the Putting Children First programme, we've mediated several times, we have regular contact with a parenting support co-ordinator and have approached the school and GP independently as well.
Admitting our mistakes and our own role in disagreements with our ex's, rather than placing all the blame on the other has opened doors for us too; we don't come across as the bitter ex or jealous NP, so people are more inclined to take us seriously when we seek help.
Counselling for the DC's. I would recommend it for all DCs involved in a separation - from a very young age; it has been excellent 
Saying all that; I don't think we've got anywhere close to 'making it work' - we lurch from drama to drama, dealing with it the best we can. We have made mistakes - with catastrophic consequences; DSD is estranged, I'm estranged from my parents and DPs relationship with his family is strained, as well. We may never be able to correct those mistakes - but we keep trying our best!