You'll probably need a new rear derailleur.
A short cage Tiagra will only wrap up 29 links of chain slack. Your 50/34 crankset takes up 16 teeth so that only leaves 13 teeth for the cassette. Anything wider in range than a 12/25 cassette is likely to be an issue. You can cheat a little bit by sizing the chain for the big/big combination and not using the little/little but, since you're looking for quite a bit more range than that, I doubt it will work.
The second issue is big cog capability. Shimano says a Tiagra derailleur won't work with cogs larger than 27 teeth before the upper pulley will start rubbing the cog. You can usually cheat a bit on that by dialing in the "B" adjustment screw on the derailleur mount. I wouldn't bet on that working all of the way up to 32 teeth, but it might.
You say that you'd like to use a cassette with a 32 tooth cog. Since you are probably going to have to replace your rear derailleur anyway, why don't you buy a Deore rear derailleur? That will handle up to a 34 rear cog and wrap up all of the chain slack without having to cheat on Shimano's specs. It'll shift fine with your Tiagra shifters.
One other thing that I'd suggest doing before you spend any money is to calculate all 18 gear ratios that you are considering. Besides the high and low ratio, think about where the overlap hits where you shift from the big to small chainring.
