You can just do an LLC with 2 members where 1 has the 'capital contribution' (and presumably the note in his name). 

The family member who agreed to lend me the rehab money and purchase money lives across the country and will be only be contributing financially.Is there a better agreement that will work better in my favor, considering I have done and will continue to do all the sweat equity?

@Rachel C.This "unfortunate millennials" who have been unable to make home ownership a reality, have no put in a valiant effort due to their preconceived notion that it wasn't possible.

If there’s ever a more significant expense, I can always contribute money back into the account to pay for it.

Agents, lenders, contractors, and other investors I look forward to speaking with you and any contribution or insight will be much appreciated. 

Start the draft yourselves: what each person is contributing to the enterprise, whether money or responsibilities, and how the income comes and goes.

Thank you in advance for your contributions! 

It gives us a chance to move slowly and learn what each of us can contribute.

Is there a min - max monthly contribution?

Bigger you go, the more you are going to need the correct vehicle or less investors are going to have contribute more capital.There are companies and people who will do the paperwork to ensure the active roles are documented and the legalities are followed.