Your intuition is your best friend. Your bf may be bipolar-being manic(high/up)doesn't always manifest in positive ways-many times when you're bipolar&you get manic, you get extremely nasty instead of giddy or overly self important. If you're not feeling safe&his own kids are afraid of him-get him out of there! You have the upper hand in this one-you own the house he lives in&it's your right to kick him out whenever you want for whatever reason. You've got some good reasons. Stay safe! I agree with others who've said that you could kick him out&tell him that if he gets help&does the work he might be able to return. If he's truly bipolar, it's up to him&him only to get help, acknowledge that he's sick&get some treatment. If you want to give him a 2nd chance be sure you listen to your intuition about his truthfulness, sincerity&any signs of real change. Many bipolars get well for a while, then stop taking their meds when they feel like they're better again&relapse, some don't see their illness or are not diagnosed correctly for years. (I'm bipolar, so I know how this works!)
It's good that you're not letting his behavior affect your self esteem, but I would suggest some stronger boundaries to protect yourself&your relationship(Bipolars are not good at boundaries.)&I wouldn't take his suicidal ideations/attempts lightly. Sometimes we do this behavior to get attention&sometimes we're honestly trying to end our lives. It's not safe to have someone like that around if they tend to get violent, belligerent, or emotional/verbally abusive. Remember safety. If he's threatening himself-he may decide to encompass you or his kids or both into those suicidal ideations. Not good&not safe! Does his ex-wife know how he's been acting around his daughters&that they're afraid of him? Another suggestion would be to convince his daughters to tell their mother about his behavior. I wouldn't suggest you to tell her yourself only because you don't want to open that can of worms&he'd possibly retaliate against you for speaking up for his daughters to someone he obviously has a chip on his shoulder about already. But, if you like&care about his daughters-you might encourage them to help themselves by telling their Mom about his behavior until he gets himself together. Best of luck to you-it wouldn't hurt for you to look up the info about bipolar that's here on PC-knowledge is power&so is your intuition. I've learned the hard way to listen to my intuition-it is your best friend!