If it's before noon, Butlers Wharf is a good bet for the best light on events (especially if you think you may take photographs and want to avoid having the light against you). Specifically, just to the west of the pier where the pleasure cruisers moor up, so they don't obstruct your view.
http://maps.google.co.uk/maps?q=pont de la tour restaurant&ll=51.504066,-0.073847&spn=0.001249,0.002052&fb=1&gl=uk&hq=pont de la tour restaurant&cid=0,0,10011792812009760707&t=h&z=19
If the children are particularly small, then you're better off slightly further east toward the Design Museum as the other locations have a wall that might be a bit too tall to see over. East of the pier, it's just a railing.
After noon, then anywhere along the Queens Walk that runs along the river past the GLA building to HMS Belfast. While there is a wall, you can get over that by standing on the raised grassed area.
Not while the bridge was moving though. It was part of a tour organised by Andrew Duncan (author of a number of London walking tour books); we got to see the usual stuff the public sees, plus various behind the scenes stuff (like the aforementioned chambers, and we got taken into one of the control rooms - I think it was an old on iirc).
