M. -
The confliction of being a working mommy! Here's my quick advice - take the job. You can always quit. Like you stated, the opportunity won't come again, and you have always wanted to do it. There is no harm in trying it and if you don't like it, quitting.
Here's my longer advice: You sound as if you want to work outside the home, but suddenly are having seconds thoughts. Think of it as the same as cold feet before marriage. It's still the right decision, but you are hard-wired to second-guess yourself. You state that financially, it is necessary to now work. If you don't do law enforcement, which you genuinely like and are eager to do, what are you going to do? Do you have something else in mind that interests you, or will you just find a job somewhere for the income? If you just find a job, how long until you resent the fact that you have to work at something that is "just a job", instead of staying at home with your kids?
As for missing out on everything....that will only happen if you let it. I can't speak for scheduling in the police departments, but I can tell you that I work full-time and my family comes first. I am a huge volunteer at my child's daycare and I attend a lot of little parties for the holidays, etc. I am blessed with a great boss, but most people I know are able to attend some if not all events that occur by knowing about them way in advance and setting up their schedule accordingly. Being involved in your child's class doesn't always mean you have to be there during certain hours. You can volunteer to set things up the day before, work behind the scenes, etc. - this will give you the sense of connection you want.
And now the holiday anxiety - my father was a firefighter and often worked on the holidays. This never bothered me because it's all in attitude - we would celebrate at different times, the families of all those on duty would get together, etc. In both police and fire work, there comes such a great sense of family and community - Christmas is only on December 25th because we "say so" - but you can celebrate it anytime. Same for all other holidays.
Whenever I am faced with making a decision that has pretty even pros and cons, I always step back and think about which option leaves the other option still open. In your case, not taking the job closes the door to the option of taking the job at a later time. If you take the job, the option of not working at a later time is still there.
Whatever decision you make, just know it's not permanent. You can change your mind, change direction, change everything any given moment of any given day.
Good luck - S.