How much do you want to spend? Keep in mind that if you really want to make this a competition gun, you'll want to have custom stock work and likely trigger and barrel work. A well fitting gun raised my score by about 10 targets (out of 100) - it is very important. Trigger work may or may not be needed depending on the gun, but lengthening the forcing cone will improve your pattern and reduce recoil, buth very good things. The downside is that work is very expensive.
Gun wise if you want to stick with autos, the Beretta 391 is good (but if used heavily enough can break the op rod). I would recommend that you go with an over under though as you can have two chokes which helps in doubles (the extra weight also lowers felt recoil which is good when you're shooting a few hundred rounds a day). Right now I have a Browning XT which I haven't had any problems with after getting the trigger worked on. However if you talk to the armorers who go to the Grand, they'll tell you that the XT is built off a field gun and isn't really set to take the kind of long term abuse that competition shooters put it through round count wise.
The BT99 is a good gun, and I have friends who use those and Perazzis who have no complaints. If I were to get a new trap gun, it would be a Perazzi MX8 or MX2000.
If your daughter has been competing I'm sure you've seen this, but there are comparatively few women who shoot trap, which gives them an advantage for winning or placing in their class (less people to directly compete against). I also want to recommend once she starts routinely shooting 80 or higher in American trap, find a way to get her on an olympic trap field. It is a very fun sport and you can get the chance to squad with Olympic medalists (all incredibly nice people). And of course if she's able to do well in Olympic trap, she may be able to compete internationally.