You should look into a cross type road bike. Capable of using larger tires for the off road traveling and often accommodate fenders. The cross bike I have also holds a rear rack for panniers. My commute round trip is 33 miles and I did it a couple of times with a back pack but a nice set of panniers with a rear rack it what you need. On the weekends I pull my 5 and 4 year old kids around in the trailer we have that you also spoke of wanting to do. For the price range you are looking at you might have to get a used bike or one of the last years models still for sale from a LBS. I was able to find a Fuji Cross used for under the price range your in. The drop type bars are nice for the longer rides but also comfortable for cruising around with the family. Hope this helps your decision making.