Duval Street is definitely not where I would take kids, especially if they are capable of reading TShirts in windows, because they can be a bit off color, and the characters you meet as well as the "music" you hear coming out of such places as Sloppy Joe's and Irish Kevin's can be raunchy at times. It is the Bourbon Street of Key West. I've spent many, many, many weeks in Key West (It's my One Particular Harbor and the place I would lay anchor for the rest of my life if I could) staying in hotels, houses, bed and breakfasts and condos and if I had kids they wouldn't be anywhere near Lower Duval until their teens. Upper Duval isn't as bad, but I'd still take Whitehead to get to at least Petronia before turning left to head one block up to Duval. My last three week stay there, the only time I was on Duval was visiting friends who were performing at Margaritaville or attending the Key West Literary Seminar.
Honestly, though, I'd walk all the way to Truman or Virginia on Whitehead before turning to Duval if at all interested in seeing part of Duval (you aren't missing much afaiac). That way you at least walk past the 0 Mile Marker for US 1, The Hemingway House and the Key West Lighthouse. There's also an incredible Kapok Tree in front of the Monroe County Courthouse that you can see. If coming from either the Westin or Mallory Square piers, you'll also walk past the Audubon House as well as Kelly's Caribbean Grill, which at one time was owned by the movie star Kelly McGillis. It's a much more interesting walk than the hole that is Duval Street, and there are a few more trees to keep the sidewalks shaded.
There's a reason the only locals you will typically find on Duval either work there or are going to the San Carlos Institute. The San Carlos is a place I recommend visiting to see their display of Cuban history and artifacts, not to mention their quiet and air conditioned bathrooms, if you must be on Duval. It's free, but they do ask for a donation. The story of it is really neat. It's between Fleming and Applerouth on Duval, just two doors down from Margaritaville on the south side of the street, not far from the Strand Theatre, which is now a Walgreens.