How do you control WHO goes to said convention
That is a good question.
The Constitution only says: 1) "on the Application of the Legislatures of two thirds of the several States," and 2) "The Congress... shall call a Convention for proposing Amendments..."
My initial supposition would be that Congress, as a part of "calling a Convention for proposing amendments" would include the qualifications for members of such a convention. I suppose they could, in their call, leave the details of each state's delegation to the state legislatures themselves, or they can try to micromanage how the state legislatures select delegates to the convention.
In any case, the Constitution says only that the state legislatures send an "application" for a Convention, but not anything about membership rules for delegations.
-PJ