@Nicholas Lehman question for you: is the plan for the original $100K be financed out at some point in the near future? For example, once you've completed the rehab /updates, or increased rents? If so, I would suggest a 50/50 equity split once both parties original investment has been refinanced via commercial loan. Also, from what I've gathered, you may be undervaluing your portion: e.g. the value of your time and efforts for research, inspections, rehab, project management, etc...
For your LLC, you could simply form the LLC under your name. After which you will then form a partnership between your LLC and your parents, perhaps in a first lien position. Most of the partnerships I've done here in Grand Rapids, MI are based on either a straight debt position of ~10% (usually for smaller deals, and depending on how many we've done together in the past. Lower (~8%) the more we've completed). Or for larger projects, we'll establish a equity position: X% of profits after both parties have recovered their original investments. In your Buy and Hold situation, you could establish the same general structure, especially if the plan is to refinance after project is stabilized. You would be compensated for project and property management (Usually 10%).
Hope this helps. Good luck...