You already have a really good handle on slow before fast, don't ever forget that!
It sounds like if she is trotting this really well then check your angle going to the third. About 30 feet out tap your inside leg and get her bending. The inside leg is NOT to shove her out, but just to say "Hey, look this way". You should do it on all the barrels, sets them up for a smoother turn.
Remember the first part of your turn is the widest, so be sure you give her a good amount of space. I like a 3/4 foot pocket at this stage, and will make an oval shape going a stride past the barrel going slow (It will tighten up when you go faster) When you reach your turn bump your outside leg so she'll step her shoulder across and finish it tight. Go in with a bigger pocket, out with a tight pocket.
If she doesn't listen to your leg, stop and haunch turn into the barrel, then circle it again. Don't be afraid to circle twice, three times, etc if you feel you need to and don't let her quit until you get a turn your happy with.
This is a lesson from my barn that shows a couple riders of different levels, I like watching it because I think it's a good angle to see how they are asking their horses to set up.