I read your post about how the Riverlands have wealth that doesn’t reach Riverrun, and how if it was better managed could also yield way more fighting men. If you were Lord of the Riverlands during a period of peace, what would you do to fix the issues it has to make it wealthier/more powerful?

Excellent question. The question sort of depends on the period, but let’s drop me in as a Tully of Riverrun. They’re in a pretty good position, being right on the Red Fork and the River Road, but they don’t have too many resources – however, the relatively undeveloped nature of the Riverlands means that a canny lord could acquire more. 

I’ve often thought that the mouth of the Trident is a hugely unexploited resource, so one of my first moves would be to build a second Riverrun (complete with a moat to wall off the third side) at the confluence of the Blue Fork and the Red. With a sufficient riverrine navy (which I would put no small amount of money into) and marine support from Riverrun, that position should be unassailable and allow me to dominate traffic on all three Forks, which should give me the upper hand on the lords of the Trident and the more easterly parts of my dominion (odd that the Lords Paramount of the Riverlands are so far away from the center of their region) and a major source of revenue from increased tax collection and a modest tariff. Riverrun-2 is also an excellent place for a cadet branch of the family and ensure that supernumerary brothers and sons can be made useful. 

Next, I would work to combine regional alliances with regional development. :

• a Blue Fork to Ironman’s Bay canal would hugely increase trade, to the benefit of House Mallister and my own (since the ships would have to pass by Riverrun-2), and allow House Mallister to better check the Freys (although I’d definitely insist that the Mallisters put some of the extra cash into more oceangoing ships – I want them to be the Riverlands Redwynes). At the same time, Riverrun-2 should ensure that the Mallisters’ new dependence on riverrine trade means a certain deference (make sure those ships’ keels are too long for the canal).
• An extension of the River Road from Maidenpool to Lord Harroway’s Town would do a similar thing with House Mooton (which is too far in King’s Landing’s orbit thanks to the Rosby Road, as we saw during Robert’s Rebellion). In addition to boosting trade along the River Road and improving access to seaport trade, this also means that I can move my armies faster to the eastern Riverlands – historically a region where the Kings of the Trident have struggled to project authority. 
• Finally, I would put some money into the improvement of the defenses of Stony Sept, both by improving the fortifications of the town and by building a canal to link the Red Fork to the Blackwater (which also provides some competition to the Mallisters) to allow me to move reinforcements down from Riverrun and create a water barrier along the southern border. Indeed, if I can manage it, I’d try to take 
• and creating a new center of gravity in the southern Riverlands since Harrenhal is such a deadweight.

All of these things should be paired with marriage alliances between House Tully and Houses Mallister, Mooton, Roote, etc. Hopefully, these links to these strengthened Houses would give me a constituency to back me against the likes of the Freys, the Blackwoods and Brackens, etc.

Third, political reform. Given so many fractious and divided vassals, I would institute a Great Council of the Riverlands as a permanent legislative assembly. This would serve multiple purposes – first, having a voice in consensus-building increases willingness to pay taxes; second, it allows me to play Houses off against each other through patronage; third, it hopefully puts some hostages in my grasp a la Versailles and Edo; forth, as we’ve seen from Alayne, lesser Houses eat up drama and pageantry. (Possibly look into a knightly Order of the Trident to further encourage this?) At the same time, to bolster my power vis-a-vis the lordly houses, I would establish city charters for LHT, Seagard, Stoney Sept, and Maidenpool as a way to create new direct relationships between House Tully and the merchant class of those places and further boost trade and economic development (and city militias are a good way to improve military readiness). 

After that, technology and culture would be key. Import Myrish and Braavosi artisans and merchants (encourage them to bring theater and the like with them), establish guilds of artificers and engineers, build some watermills. Lobby the High Septon to upgrade Stoney Sept to a Great Sept with a Most Devout, maybe build up Humphrey Teague into a Riverlands quasi-saint a la Baelor the Blessed and encourage pilgrim traffic. Build church schools in the cities and towns to expand literacy.