The recommendation for tires is that they last about 5 years then will start to age regardless of the mileage. Most vehicle tires wear out from use before the 5 years.
Aging out is a common problem with trailers because they sit for so long even though the tread looks good. In your case it seems your vehicle sits for long periods and the tires are not used very much (low mileage) and this can occur. Stems can fail for all kinds of reasons, many times because the right stem is not used (low pressure stem for a high pressure wheel, for example). Many members here opt for the metal stems which are much stronger than even the rubber high pressure stems.
To check for the age of your tires, look for the DOT code. The last 4 digits are the date code (2 numbers for the week and 2 numbers for the year). The DOT code MUST have 8 or more digits. If you see a DOT number with only 4 digits, then look at the other side of the tire for the longer more accurate code. A DOT code with only 4 digits is an ABBREVIATION of the correct DOT code.
Here's a sample link on how to read the DOT code:
http://www.tirerack.com/tires/tirete....jsp?techid=11