Richard,
I'm not sure what brand the tires are but they aren't the Missions because my son-in-law had the Missions on his 5th wheel and got them all replaced. When he looked at my tires he said I should be OK because I had a different brand.
The problem isn't with the tire, it is with the rubber valve stem in the rim that you put the air in thru. I honestly don't know how you would check them because I wiggled all the stems when I checked the air not 2 hours before I had the flat on the road. The valve stem comapny is Tech International, the Recall is NHTSA Campaign ID Number: 08T018000.
Here is a link that I just found that will be very helpful:
http://www.tirevalverecall.net/
This site has pictures of what to look for-wish I had looked for this site before I had the second flat! (This isn't the link that I had originally found a week ago after the second flat). I'm wondering why the tire store I went to to have the valve stems replaced didn't say something about the recall. They knew why I was having them replaced and they are listed on this web site.
This is link to the fist site I found:
http://www-odi.nhtsa.dot.gov/recalls...e&refurl=email
Hope this additional info helps.