The Tiagra cranks changed from the 9 speed versions to the 10 speed ones. The 10 speed ones changed the bolt pattern that unfortunately limits the smallest granny gear to 30, earlier versions had a diff bolt pattern that allowed changing it to a 26.
I am not super familiar with crank sets, but there are other 10 sp bikes out there that use cranksets smaller than 50/39/30. A good knowledgeable bike store can give you some options.

also, concerning changing your old chainrings to new ones, again, you would have to get informed info about what requirements are needed for 10 sp chains in terms of what chainrings you could buy and use on your existing crank. In our household we only have up to 9 speed, and I do know that early 90s 7 speed chainrings work fine going onto 9 sp cranks, I put an old 28t granny onto my wifes 9 speed bike 3 or 4 years ago and it worked fine.

re gearing, I am more familiar with "gear inches" for figuring out if a given gearing is low enough from my experience carrying a full load up mountains, but without getting into numbers, using a triple that has a granny of at least 26 and a rear cassette of at least 32 is just going to be more enjoyable for you and your knees.

and dont forget, there are mountains and there are mountains. Some mountain roads have reasonable gradients that go on for ages, others have short, really steep bits that are a real bugger.
Unfortunately, until you have toured loaded up mountains with a given bike+load weight on a given gradient, you won't really believe what we are saying here.