Correct usage for 跟。。。过不去
This expression means 'to make life difficult for', 'to make it unpleasant for' or 'to pick on', just giving a few possible translations from the top of my head. Therefore your interpretation is correct. I am not sure what you mean by 'Is there a particular emphasis in this?' Emphasis in what? 

As for your second question - yes, it can be used either reflexively or transitively (on another person). There is nothing that stops you from doing that. 

Does the meaning change in reference to an action done to oneself?. No it doesn't. You have correctly observed that 何苦呢 (why torturing yourself over this?) means the same as 为什么跟自己过不去呢 (why making it difficult for yourself?). 

As for your examples, 


别提他妈妈的身体，你想跟他过不去吗？ - It's ok, but needs more context to make more
sense.
别跟我提那件事，否则跟我过不去。 - Missing a subject. Better served with:
别跟我提那件事，否则*你就是*跟我过不去。
你天天喝醉，为什么跟自己过不去呢？- It's ok, but would sound more natural by adding the adverb 都 between 天天 and 喝醉.  I assume the subject is using alcohol to
forget his/her troubles. If not, then more context is required. 


Just a side note, variations of this include 和。。。过不去 and 同。。。过不去.