Here's the requirements:
http://www.statutes.legis.state.tx.u...11.htm#411.172
The 2003 misdemeanors should not be a problem, the code above specifies convictions within the last 5 years of certain misdemeanors is disqualifying.
The 2007 misdemeanors may be disqualifying, depending on what they were for, until they are over 5 years old.
I guess I would wait until 2012 (5 years after the 2007 misdemeanors) to apply for the Texas CHL.
IANAL.