I think that the letter should clearly state what you want from him, and what you plan to do.
Like in the first version- When you communicate angrily and threaten us, I fear for our safety- good, it tells him what he does and how it makes you react.
If you come over uninvited, I will be forced to protect myself- you laid down a boundary here, and explained your consequences- good!
You tell him that you want him to demonstrate his genuine interest, thats good, what do you think about telling him HOW he would do that?
I dont like the ambiguity of the 2nd letter. I think that theres alot to be said for clear, concise, factual information.
I guess I gave the wrong finger to the wrong man...