Crothian said:
I have one character in my campaign who has many feats to make her Diplomacy and Wild Empathy rolls very high. I don't want to negate these abilities but at the same time I don't want her rolling her way out of every tough situation or fight.
How have other people handled characters like this?
Come on! There are so many situations where you simply can't count on those 2 abilities

There are mindless creatures or creatures who don't respond to talking, creatures who don't understand your language (or don't have one) and at the same time they are not animal or magical beasts to be affected by Wil Empathy. What about Undead, Constructs, Plants, Elementals...? There are also high-Charisma creatures who may be better diplomats than your player's PC, like some Outsiders or Dragons or Feys.
Also many situations simply can't be resolved by parlay. An ambush typically starts before you have the chance to speak, and you anyway take a -10 to Diplomacy if you do it as a full-round action (otherwise it takes a minute) to change attitude. Considering that the DC to turn hostiles NPCs to Friendly is 35...
As the DM, your chance to increase the DC with circumtance modifiers is very wide, and you can come up with many reasons why a NPC won't change his attitude. Perhaps he was previously intimidated by his own master to fight against you until death, and you may rule that you actually need a Diplomacy result higher than the master's result. In this way you can prevent the players to skip an encounter you really don't want them to avoid.
That said, if your player has chosen his PC to be a top-diplomat, it is best to reward her effort often. Per the DMG you may still award XPs and they are still shared by all PCs. You will have less fights, but that simply means that your campaign will go faster
Finally, I also think that having the party resolve many encounters without fighting makes the game both more realistic and more similar to novels adventures. Especially if they are playing good characters.