How do divorced men date again?

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I'm 33 years old and been with my ex wife since the age of 22. When we divorced I was 30 with 3 kids. I dated a few women but most didn't understand the dynamics of being a divorced male. For instance my career come first, followed very closely by my kids! If I don't work they don't eat. I recently moved to NY for CA so if they call that a priority. A grown shouldn't be trying to compete with my kids over my time. If I talk with them for two hours it doesn't mean I don't want our relationship to stand still. If I chose her over my kids I'm a deadbeat, however if I choose my kids I could lose her.....no tell me what's a fella to do?