Alice, if you're serious about a rental and you really want a home for your family, call a Realtor TODAY and ask them to send you a REAL list of ACTIVE and AVAILABLE homes in your price range and area.
Searching for 'Active' listings on Trulia, Zillow, etc. will just lead you to nothing but frustration and despair. These sites simply don't take the time to update the listing inventory to show what's 'Pending' or 'Closed'. I'm not just saying that; it's true. Ask any agent on this forum. The only real way to find VALID and Up-To-Date information is from the Multiple Listing Service (MLS).
I understand your desire to simply search on your own and not be 'bothered' by a Realtor, but believe it or not, I'm sure that any one of the agents on here would be more than happy to assist you with NO pressure and NO obligation.
I'll bet that you could be out looking at rentals as soon as this afternoon or tomorrow morning IF you called one of the agents that have responded here on Trulia. Wouldn't that be nice instead of pounding sand looking at homes on Trulia, Zillow, etc. that are already rented?
Hope that helps to encourage you to seek some assistance from an agent! You won't be disappointed!
Realty ONE Group