Yes, you will be able to continue to use your Tiagra shifter & front derailleur.
Yes, it is a fairly simple change:
- replace the crankset & BB
- shorten the chain by a few links
If you have a Tiagra crank, I believe it probably uses an Octalink V2 BB -- that's the same type that Shimano's Octalink MTB cranksets use. While it would seem expedient to simply continue to use the existing BB, your BB's spindle is probably 118mm long ... and, you only need one which is 113mm long.
Does 5mm make a difference? Maybe, yes. Maybe, no.
Probably, not!?!
- Some people fixate on the Q-factor ... it matters to some extent, but not as much as some people would like to think, particularly since pedal-type and how the cleats (if you are using clipless) are mounted can effect the foot placement on the pedal.
The reason it may not matter is because the "factory" Q-factor on a MTB crank is closer to 170mm ... on a Road Double it is between 145mm to 150mm ... on a Road Triple it is 150mm to 155mm. Simply installing an Octalink MTB crankset on the BB with the longer spindle will result in a Q-factor of 175mm ... so, figure your pedals will be 10mm further apart on each side than they are at the present time OR 7.5mm if you change the BB.
So, again, probably, the spindle length will probably not matter as long as you lower the saddle by a few millimeters.
- I am presuming that the front derailleur's cage will swing out far enough
If you think the 2.5mm in the Q-factor is going to make a difference, then you can buy any MTB crankset & BB which strikes your fancy.
BUT, do you really need THAT LOW a gear ratio?!?
19 inches would be pretty much the same as walking.
BTW. You can get Shimano MTB cranks which use Octalink BBs from eBay ... you will need a crank puller if you don't already have one ... if you have an older one OR if you don't get one for Octalink-and-ISIS BBs, then you can insert a "slug" (e.g., a couple of pennies) against which the crank puller will press.