The ability to blow the ball right past weaker batters at a higher speed.
This false "skill" is only a temporary feel-good thing for dads. If your DD has any desire to progress her game to increasingly competitive levels, flat pitches - regardless of speed - will eventually become homeruns, and your DD will also increase her risk of getting nailed by a line drive.
Have the correct spins on pitches so that hit balls are easily playable.
There's never any guarantee, but correct spin (=desired movement) usually results in a desired result. Pitch to the batter's weakness, and place the pitch with an intent to get the batter to hit the ball to a desired location. For instance, in an obvious bunt situation, force the batter to work with high pitches which are more difficult to get down cleanly.
Have a very convincing change-up.
This should be a given for any effective pitcher! Pitchers rarely succeed at a competitive level without a convincing changeup. And slow-arm changeups ARE NOT effective against good hitting.
How much does batting ability play into decisions?
A pitcher who can also hit is all that more marketable. The only catch is some college coaches do not bat their pitchers. It's just a preference thing for them. All I can say is - Jennie Finch helps her team by hitting... 'nuff said.
How about ability to play other positions?
Views on this vary widely, but it really comes down to the pitching ability of your DD. Can she be the workhorse pitcher for a team? Is she the absolute #1 starting pitcher? There's no secret here - you'll know it and so will the coach. If that's her role, she's probably resting when not pitching, especially in 90 degree weather. But, just like hitting skills, she's a softball player - so developing good infield/outfield skills should be part of her routine. You never know...