Which leads me to your "real" question, which was, quote:"What can I legally do to take away the rights of the man who refuses to do right by his child?"
While he certainly won't win father-of-the-year (or even good person of the day), what the hell does that have to do with trying to legally take away his rights as a father? Don't you realize that we're not talking about a light switch here, where once they're taken away can pay the court $20 and get them back. Aren't you making a huge assumption that he'll never learn from his mistakes, take responsibility for his actions, and turn his life around?
You've got your priorities all screwed up. You have a responsibility to protect your child, but that's it. There hasn't been any mention at all that he is or ever has been a danger to his son. Moreover, arrested and charged with various offenses is a far cry from being convicted (the "three months ago" thing you quote).
Your "taxes" thing has me puzzled...why wouldn't you list him as a dependant (regardless of what the father does)? If the IRS catches two people claiming the same dependant, it should be a snap for you to prove you've had custody for most of the year, and therefore the right to claim him as a dependent.
If your young son is in danger, than do something about it. If this new man in your life has taken a father-like role in your son's life, that's great. But, it sound like you're more interested in getting back at that the father for his failings (and Jeanie is assisting in), than doing what's best for your child.
I'd like to suggest that what's best isn't trying to "steal" custody from the father, but simply asking him if he'd be willing to give up his custodial rights. If not, than that's your answer. If so, then your problem is solved.
But, you'll never be able to convince me that it's not possible for the father to turn his life around, and do the right thing (and be a good father). People who truly know me here on Custody Reform can attest to this statement as being factually accurate.
Keep your child safe, happy, and well taken care of. If his father is going to dig a hole for himself, let him. There's little point to you throwing dirt into the hole.