What part of PA are you going to be in and around what date? There are at least three semi-decent rodeos that I can think of that have barrel racing. They all take place over the summer (one in July, the other two in August), and are in Western PA.
My favorite is at the Flying W Ranch in Kelletville. They usually have a rodeo around the 18 of August or so check their web site at theflyingwranch.com. It's a nice scenic area up there if you've never been there. We have a cottage in the area, so I'm up there often.
Hope this helps!