As a child of divorce (my parents divorced when I was four), I can personally say that divorce can be, or maybe always is, hardest on the kids. It should be a decision of last resort when kids are involved and very clearly the "least bad" of your options in a bad marriage.
That said, it does occur and divorced dads have special challenges.
Divorced dads have a lot to prove since they will likely take at least half the blame for the break up of the family. If you're a divorced dad, you are also likely to have lost custody of your kids. You're less present for them everyday and need to make the most of your time with your kids.
Divorced dads should follow all the tips for regular dads, but should be especially attentive to these.
• Never date or marry any woman who wants to put herself ahead of your kids. It doesn't matter how pretty, sexy, wealthy, intelligent, funny or seemingly caring she is. When you had kids, you made a covenant to put them ahead of everything. When all else fades, your relationship with them will be the strongest love of your life.
• Never compare siblings. This goes doubly for step-brothers and sisters. If you compare them for any reason, at almost any age, you give your own children a reason to doubt your love for them.
• Make twice the effort to be at every game, school play, and birthday.
• A corollary to #3, move or stay wherever your kids live. Other places may beckon but your place is close to your family.
• Never discuss your ex-wife. This last might be especially difficult given the circumstances for your divorce. However, no matter how great the joy may be in the moment to say something negative about your ex-spouse, you will gain nothing from it in the long run. If your spouse is as bad as you say, it will be obvious to the kids. If not, they will hold it against you.
Every divorced dad has to carry his own grief and try to begin a new life again in the world. Remember that you are still a father. Taking care of your children during this crisis is your first priority. It's the only way to break the inertia.