I was in the ChEAR squad when my wife ran the 2011 Princess Half Marathon. The amenities for the different levels have changed over that time. I believe I did the Gold level which included the T-shirt, a folding chair-like sitting apparatus, and the special viewing areas both in front of the castle and at the finish line. Oh, and don't forget the Mickey head clappers (my girls loved those). I think the price at that time was around $50. For me, the best part of the package (or any level package that includes these) were the viewing areas which were well placed and easily accessed. The viewing area in the front of Cinderella castle gave the viewers an unobstructed view of their family members as they emerged from the castle, ran past the viewing area and continued into Liberty Square. At the finish line, bleachers were used for the viewing area also providing a good view of the finish.
Is the Platinum level worth the money? I think the answer depends on how involved in the race your family will be. If they are only going to see you finish (not start) the race, I would have them plan to be at Epcot 30 minutes before your anticipated finish. No Epcot ticket is required to enter the finish line area (will need the Gold package to use the Grandstand seating). If the family will be there for the start and the finish (at Epcot) but will not follow you to the Magic Kingdom, then certainly a heated tent does sound appealing particularly considering the 8 month old. The average low temp for January 12 is 47 degrees; it is possible the heated tent will not be necessary (of course, the record low is 24 degrees for that date). The other Platinum amenities (character greetings, brunch, etc) are also appealing if the family is staying at Epcot while you run. All that being said, the $420 pricetag for your wife and three children seems pretty steep to me. If your family is going to chase you to the Magic Kingdom and back, I would not purchase the Platinum level because they will have very little time to enjoy the amenities. The chase includes a Monorail ride to the TTC, change trains, Monorail to the Magic Kingdom, sitting in front of the castle waiting on you to arrive, Monorail back to the TTC, change trains, Monorail to Epcot, walk to finish line to see you finish. Depending on your anticipated finish time there is likely to be very little time to enjoy the Platinum amenities (and all that rushing around tends to keep people warm as well).
I apologize for the long-winded answer but I think there are quite a few variables to consider before purchasing a ChEAR package. Good luck with your training. My wife and I will be there running the half marathon together this year.
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per person, is quite steep. 
