About subjunctive mood

"Should" wouldn't be used by most English speakers/writers. Since "if" signals that the condition might not occur, we already know that.

Remember, the subjunctive MOOD is a trait of VERBS alone, and this auxiliary/helping verb is being used exactly like a German "modal auxiliary" to make up for this:

the ONLY verb in English which has a change in its base form in the subjunctive mood is "to be"

Also "should" can mean "ought to"; more clear is

"If you happen to go there, would you please ask her to call me?"

The example should--in the sense of "ought to"--use "would" in that way in the second part.

Yes, it does not need the word should there ... it can be there if you want, but it doesn't have to