How can I make my fried potatoes not fall apart?
A few possible ways, which can, of course, be combined:


Use waxy ("new") potatoes. These potatoes have a lower starch content, as well as a different ratio of starches (more amylopectin) which helps them maintain their shape.
Microwave then cool the diced potatoes rather than boiling them. Do this in a microwave-safe bowl with microwave-safe plastic wrap over the top. This process should also help maintain potato integrity while cooking them through.
Fry them in small batches in vegetable oil (or another high-smoke-point oil) at med-high to high heat (depending on your pan/stove combination) rather than the lower heat required for frying with olive oil. To get a nice brown crust, you're essentially searing the outside of a pre-cooked potato.