Not sure exactly where you are, but here in Australia, the background check to be a police officer is very thorough. I know that when I was looking into joining the force it stated that you couldn't have had a driving offence, so that cancelled me out straight away.
Also, something for you to consider is; even if you did get the job as a police officer and you lost your cool at work and something bad happened, if that went to court what would the ramifications be for yourself because you didn't make them aware fo your condition?
I hope you can join the force if that is what you really want to do, and I hope for your sake and that of your families that nothing will go wrong, but it would make sense to look into that a little further.
Tammy