Since Kanchanaburi is my second home town I know that even if you will have a couple of busy days here, you will most certainly also be in for some very nice experiences.
To me, though, it looks as if on 'Day 2' it might be pretty hard for you to make it all. Hellfire Pass is 60 km north in one direction (same way as the Tiger Temple), but Erawan Waterfalls is 60 km north in another direction. Depending on your preferences I might want to skip the Hellfire Pass despite it historic value, and go to the beautiful Erawan Waterfalls in the morning (don't forget your swimwuits for a swim in the water) and be back for a trip to the Tiger Temple in the afternoon.
But you may want to contact one of the local tour agencies, like 'Good Times Travel', for further information, or you can have a look at the link below.
Enjoy your stay here in Kanchanaburi!
Kanchanaburi-info.com: destination guide to Kanchanaburi Province, Thailand