Hi Jackie!
Thank you for bringing your question to the Disney Parks Moms Panel. We actually managed a very similar set of logistics during this past
Disney Wine & Dine Half Marathon Weekend! We had morning reservations at Chef Mickey's and my toddler was running the runDisney Kids Race.
The runDisney Kids Races start at 10:30 AM, but they are grouped into smaller increments based on your child's age. When the Digital Event Guide comes out for your race you'll have a better idea, but until then I'll use this past years
Disney Wine & Dine Half Marathon Weekend Digital Event Guide as an example. Under the runDisney Kids Races, you'll see the 1-4 year olds raced from 10:30 AM to 11:15 AM and 5-8 year olds were from 11:30 AM to 12:15 PM. So depending on the age of your kiddo you may have a little more time.
I think it may be a tad tight, but I certainly think it's possible! I would recommend arriving 20 minutes early or so for your Advanced Dining Reservation and while there is no guarantee they may be able to seat you a little early. I would shoot to leave Disney's Grand Floridian Resort & Spa and be on the runDisney bus by about 9:30 AM. I think that'll give you enough time to get to ESPN Wide World of Sports and through security in time for a 10:30 AM start. If your runner is in the older range you can push that back a bit more!
Please let us know if you have any questions!
-Lindsey ºOº