A newly divorced man will want the comfort of a relationship but may want independence at the same time. He needs time to feel his way through to a new way of life. His past relationship(s) may have cost him in many ways. He may be unable or unwilling to tolerate your needing attention at times. If he's been married a long time, he may want the opportunity to look around and date a few more people.
The biggest challenge of dating a divorced man with children is that you will not be his priority. His children and his job will likely take precedence and if his children aren't a priority, take a look at his character. This is a red flag. He will have bigger bills to pay so he will have less discretionary spending money than he had in the past. He will also need alone time with his children to show them they are a priority and help stabilize them.
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Please encourage this without complaint. He should be in relationship with you for awhile, at least a few months, before introducing you to them. Don't be upset by this. He should not introduce you to his kids until he knows the relationship with you will last for awhile.
Children of divorce have been through enough without becoming attached to a person who will soon disappear. Children need time to adjust to their parents living separately before seeing them with someone new. If the introduction is rushed, it may undermine their relationship with you indefinitely.
Women have a tendency to give up a lot to support the man they love and expect the same in return. Understand he may not be willing or able to reciprocate at a particular point. Men in general operate differently. A romantic relationship is important but not as important for men as it is for women.
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So, if you've fallen for a divorced man, make sure you prioritize your own life: your own children, career, goals, interests, friends and activities. Be supportive but not dependent. Independence is attractive to emotionally healthy men so you will not only be healthier yourself, you will attract an emotionally healthier mate. Don't chase him. Let him come to you. Final words: proceed with caution.