If "within reach" means "within a single movement range of the target", then the target can't escape the "within reach" range unless they have more than double the Duelist's movement, because the Duelist's Challenge cuts movement in half. I think this is more what you're going for.
Frankly, I like it, but I guess my understanding isn't clear on when Dimensional Anchor is applied, since "within range" is relative.
While I can see this, and I wouldn't necessarily suggest giving Improved Uncanny Dodge to the PrC outright, a Rog4/Bar2 gets Improved Uncanny Dodge just from getting Uncanny Dodge from two different sources, whereas a Rog4/Duel4... Doesn't. Instead, they get an Uncanny Dodge they can't use with their armor.I could put it into a separate ability and allow the scaling, but really, I'm not sold on the Duelist actually needing improved uncanny dodge. It's one of those things that would be nice, but not particularly necessary. On the other hand, Uncanny Dodge is one of those things, as someone else put it, is necessary for the class to function. It wasn't put in to be an extra power boost so much as to ensure a duelist doesn't get splattered because he didn't have it, if that makes any sense.
I think it just makes sense from the perspective of a character that already has Uncanny Dodge applying their already intuitive knowledge to the training that they are receiving as they continue to progress, as base class combinations already do. It makes sense from a progression standpoint and is consistent with what Uncanny Dodge already does, and while I guess this isn't technically Uncanny Dodge, it does give some benefit to a dedicated duelist choosing Rogue over Fighter, since Fighter gets Uncanny Dodge from this anyway.
To be perfectly honest, I never liked Mobility. In melee combat, I always make it a point not to provoke (instead using five-foot steps or Acrobatics/Tumble checks to get away), so Mobility is more or less a dump feat. I would love if it were gone.I can see your concern with a non-fighter having trouble entering the class... what if instead of making combat reflexes a bonus feat and taking it off the prereqs, I bumped the prereqs down to requiring dodge instead of Mobility.
That way a non-human non-fighter could go 1) Weapon Finesse 3) Combat Reflexes 6) Dodge, and qualify at 6. There's nothing in the class that really requires mobility, it is merely fitting, on the other hand, combat reflexes is a pretty central part of making the class work, and I'm leery of handing out further power increases, even something as small as an extra bonus feat.