There is one way which makes the transaction very cut & dry and fair for all because you both, in essence, own this business and therefore want to ensure the `business` is getting the best deal for its dollar.
a. They can qoute the "JV" (you and them) how much it will cost to do the work and that becomes part of their financial contribution (as if it was a cash infusion) that is returned to them upon the ultimate sale of the proeprty (or re-finance). key is to determine whether the quote is accurate, and you do that by getting other quotes as comparison.
b. If it is cheaper for others to do it, then it makes sense from a business perspective to choose the other contractor (or have the partner adjust theirs accordingly).
Trust that gives you perspective on the situation. Remove the `personalities` from the equation, do what`s best for the business (JV).