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I have the original Michelin XCX tires on my 2002 Buick Rendezvous which has almost 36,000 miles.  There is some cracking on the sidewalls and, in one small area (approx. 1"x1") the rubber has been worn/torn off.  The tread is wearing more on the outer part of the tire (apparently from underinflation) but the middle tread is fine.  A local auto repair/service shop (that I trust and have used on several occasions) says they are dry rotting, must be replaced and that they, personally, wouldn't drive them on the highway.  On the other hand, a large nationally known retail store that has an auto shop (that I also trust), says the tires are fine (actually, they say they didn't see anything unusual other than where the tires probably rubbed against curbs) and that we should overinflate the tires a little so that more of the center tread is used.
I have two small children and if there is the slightest chance I could have a blowout with these tires, I'm getting them replaced.  Obviously, if there is really no reason to replace them, I won't.
Can anyone with experience on this tell me what they think?  If needed/helpful, I can post photos of the tires.
Thanks so much in advance for your opinions/expertise.