From my own experience, it is NOT worth trying. My parents love my very much, but REFUSE to accept mental illness, and that's not going to change. However, I am financially independent, so it was easier for me to just cut down my communication with them, and that doesn't seem to be an option for you. Take comfort in knowing that this is a common problem among people like us - family not understanding us.

One option for you is to explain the condition in simpler terms that they might understand: For instance, you might say you have an anger problem (or anxiety or depression). Anger is so fundamental, and most people on Earth can understand it and empathize with people who suffer from it. So, in other words, instead of bringing up the diagnoses like Bipolar, bring up the symptoms (like anxiety/depression), which are easier to understand.

Explain it to them, calmly, in their terms, and that you need their help to get through it. If they insist that you can overcome it with will power, explain that you have tried very hard, and that it's not as easy as they think it is.

The key is to be calm but serious, don't lose your cool when talking about these issues. I understand that you are frustrated with them for not understanding you. But, from life experience, the one universal truth is that messages conveyed calmly make it across to the other side, and messages conveyed heatedly end up in the toilet.