While my own experience doesn't quite match up to your question, here's what I have experienced. 3 of my 5 race weekends have been solo, including my only WDW race weekend. It's certainly doable to work a vacation in before or after a race. Just understand that the runner(s) and the family may have to make sacrifices. From reading your plans, what you want to do doesn't seem like too much, but the trick will be figuring out what you want/need to do after the race versus what your family wants/needs to do in the parks. The nature of a race means an early bedtime the night before the race and getting to the park late the day of the race. That may be at odds with what what everyone else wants to do.
Because of work conferences, I had to run the 2012 Wine & Dine at the end of the Disney World visit instead of the beginning. On top of that, I caught a cold right at the beginning of my taper so my running suffered. I flew into Orlando on Monday, did normal parks touring on Tuesday through Thursday. Packet pickup Friday morning at the Expo and touring the parks afternoon and evening. Rested Saturday morning before realizing that I was going stir crazy so I headed to Epcot to do very light touring and a whole lot of sitting down inside attractions with minimal waits in line to preserve my legs in the afternoon before heading back to my resort around 4:00pm to prepare for the evening race.
I finished the race and stayed to the end of the after party. Slept in the next day until about 1:00pm before heading to Epcot for a late lunch and Illuminations. I basically wandered around World Showcase and took it very easy. I stayed for Illuminations, but I don't know if I would have stayed had it not been my last night in Epcot, which is my second favorite Disney park behind
Disneyland.
Monday was my last day and I spent all day at the MK from rope drop until the end of
MVMCP. There were a few moments when I really felt the exhaustion, but soldiered on because it was my last day at WDW. When I left the MK at the end of the party the adrenaline vanished and I was exhausted. Flew home to the west coast the next day and then had 2 very early wake up calls for a work conference the next 2 days. Honestly, that's a rough way to do it. Recovery from both a long distance race and a lengthy vacation gets impacted with earlier than normal wake up calls. Looking back, I would have been better off touring lightly the Monday after the race as well instead of trying to go commando one more day. However, it's also doable if there's no other option.
For the 2015 Rebel Challenge, my mom decided to join me. While I have an AP, she only had a one day ticket. What you need to pay attention to with the family component is the runners race needs vs the family's park touring wishes. I start to unwind the night before a race between 6 and 7 at the latest and try to have lights out trying to go to sleep no later than 9:00pm. This wasn't a problem because the hotel put us in a 2 room suite, so I had the total quiet and darkness to rest in my room while my mom could relax however she wanted to in her room both nights. However, if there are not separate rooms, you could be looking at some challenges to your pre race rest.
If your family wants to tour the parks, they may want to stay out late. When they come back, you may be woken up. If they come back with you and go to bed when you do, it's still something they have to do. One solution I've heard others recommend is that the runner get their own separate room for one night. That way the runner doesn't majorly disrupt family touring and gets the rest they need. However, this comes with extra cost for all the obvious reasons.
The second challenge comes from the day of the race. Having run 13.1 miles you will be tired. Your family won't be as tired. While light touring of the parks is a good way to recover since you keep moving and don't allow the muscles to tighten up, you will still be really tired. Your family may want to tour more intensely than you do. They may be up for running around like we often do at Disney. You may want to choose what you ride based on how long the wait is and how the long ride is. The soreness and exhaustion will also continue into the day after the race and that may be another easy day for you while your family may want to go back to full speed especially if they're used to it.
As a west coaster, I never actually want to stay offsite at Walt Disney World. Setting aside all the perks of onsite, I believe that staying onsite helps make Disney World an equally tremendous, but different experience from Disneyland. Personally, for a race weekend, I cannot fathom staying offsite because of all the hassles that come with getting to the race, parking, and time costs. Time is at a premium enough that early in the morning if you're staying onsite where Disney provides buses that take you to the race start and back to your resort.
In the end, what you want to do can be done and fairly easily at that. Just keep in mind that everyone has their own agenda on vacation and compromises will need to be made.
