The actors were recalled for additional scenes and dialogue. The filming of later films went on while earlier films were in post-production. I don't know how that fits around release dates.
I suspect the director wanted to see more of her. I don't like her performance much myself. She really only belongs in the Lothlorien scenes of the first film.
In my view the extended edition of the first film makes the biggest improvements. It is better balanced, and the additional scenes add to the characterisations. They also fill in some plot-points, eg about the elven gifts.
I reckon there the Director was just trying to make a better film. For the later two EEs, the Director seemed to be trying to please the fans by sticking stuff in whether it improved the film or not. Both the second and third extended editions could be improved by cutting, in my view. The extra scenes should have go into a "deleted scenes" section of the DVD rather than being part of the movie.
I think the middle film EE is better than the theatrical release, but frankly there is so much damage done to the books that nothing can really rescue it.
I think it is the best of the three. It has more of a journey, both literally and metaphorically. There is more variety of locations, eg Shire, the elves in Rivendell, snow-covered mountains, the depths of Moria, the different style of elves in Lothlorien. We see Isengard both before and after it is despoiled. This variety of location is reflected in atmosphere and tone - where the later films are relentlessly dull and dark, the first starts with some lighter scenes. Although much of it is on a small scale, it has some of my favourite bits, eg the Nazgul entering the Prancing Pony. The Party fireworks alone are worth the price of admission.
It just seems to have more going on. Where-as the second two films are both dominated by the big battles at Helms Deep and Gondor.