Sounds like a productive visit, but I know that PT "homework" can be a bear to do. I always start out all motivated and then start slacking over time...
Another reason standing to climb tires you is because you're bearing your body weight -- I believe I've read it's something like 25% more effort (maybe more) than seated climbing. So it's not just muscular. I can only do it for short periods of time, but with the way my Trek is geared (12-25 in the back, higher than any bike I've had in decades), I end up standing more than I'd like to avoid having to use my granny gear.
Good luck with the PT!
Emily
2011 Jamis Dakar XC "Toto" - Selle Italia Ldy Gel Flow
2007 Trek Pilot 5.0 WSD "Gloria" - Selle Italia Diva Gel Flow
2004 Bike Friday Petite Pocket Crusoe - Selle Italia Diva Gel Flow