How do I bring this up?

I'm pretty sure my mother has bi-polar disorder. She's in complete denial and in the past has refused to get help, besides having to be admitted to the psych ward once in high school and nearly being admitted again a few years back. When my father was with her, he said she would only call it a "chemical imbalance" in her brain, and refused to say whatever the docs said it was out loud or tell him.

I'm sure you've heard all sorts of stories from children of parents with bi-polar disorder, so I won't go into much, but I don't know if I can do it anymore. I'm so sick of trying to do my best to keep her happy and calm and watching her paranoia and accusations and sudden bursts of anger continuing.

I really want to talk to her about getting help, but the moment anyone mentions her possibly being mentally unstable she freaks out. I'm scared to ask. If I don't ask, I might end up becoming suicidal again. It's so, so stressful, and now that I'm older and I understand more that what she's been doing to me and my sister is unusual and I shouldn't have to deal with it...it makes it even harder to stomach.

I'm worried that when I bring it up she'll get angry and go into rage-denial like she often does in other situations and kick me out of the house or say really hurtful things again. But if she does that, then my little sis will be the only one living with her, and she just can't deal with this stuff. I've always taken the brunt of it for her, and if I'm gone, I don't know if she could bear it.

My father divorced her because he can't deal with it, and I've come to him multiple times to tell him she's having a bad episode and we need to stage some sort of intervention, but (like the sort of guy he is) he blew me off and ran away from the problem. Which was the point of divorcing her, so I know why, but at the same time, I'm 16, not an adult, and I'm hitting the point where I can't "be the better person" anymore.

Can you think of any way to bring this up to her that wouldn't instantly infuriate her? Is there any way I can force her to get help that won't backlash on my sister?