Finding babysitters is always tough! We moved here last October and are LOVING Fort Worth. We also have a 3.5 year old and an 18 month old.
What we did was join the YMCA. Great way to kill a couple of hours, meet people and stay active. They have childcare and they're always wonderful, at any branch. We use their Parents' Night Out the last Friday of every month at the Northwest Y on Boat Club Road. Great way to get out for dinner, get away for a few hours and know that the kids are safe.