"Go by yourself. I don't want to go!"
一个人 is not accepted by DL. I've been and this question 3 times now and got it "wrong" each time because i forgot DL insists on 自己 here. So annoying!
This feels like it should have a 吧 after the 你自己去 to soften it. Of course, if we wanted to be really impolite/emphatic we could always say, "你自己去呗，我才不想去（呢）!" But even Duolingo's sentence already sounds as if we are hopping mad at the person we are speaking to.
The exclamation point in the sentence indicates an imperative so I do not believe it is necessary to use 把 to soften it.
It can still include the exclamation mark, using 吧 with it is different from using it alone.
It sounds like the speak has already decided what he/she will do. So why is 想 used instead of 要？
想 and 要 overlap on the "want to" end of the spectrum, but 要 strays toward the "need" end. Thus, 想 is used when a speaker wishes to sound less certain or demanding.
Why is 自己去我不想去 wrong? And how do you tell from the Chinese that it is an imperative?
There is no grammatical command form in Mandarin. A declarative sentence beginning with 你 or 你们 can be understood as a command in context. Thus, 你去睡觉 is an imperative when said to a friend who is nodding off while watching TV. You can soften such a sentence by adding the final particle 吧 ba or by using words such as 应该 yīnggāi before the verb phrase. Negative imperatives often use 不要 bú yào or 别 bié, both meaning 'don't'.