It sounds like whatever style you're training, it doesn't have two-weapon forms as part of it? That would be the first thing to look at. If you're training without a form/teaching that includes two weapons, you're basically re-inventing the wheel and would do best by cross training in something that already has it.
Conceptually, you're not "doing two things at once" you're doing one thing, like how if you have a stance that involves stepping forward and striking - it's one movement, not two. You practice it until the compound movement is one thing, and in the same sense, the movements for two weapon styles are "one position" or "one movement" as far as the way you process it once you've ingrained it.
Filipino martial arts, silat styles, Kung fu with two dagger forms, all of these handle the issue quite well and solve the two first hurdles: not injuring yourself in the process and having functional attack/defense through your movements. After that, it becomes a lot of two person drills to get your range and timing down, and then from there actual live sparring. (Edited to add a youtube video of Heaven 6 broken down into clear steps.)
Alternatively, if your style has a long weapon + a parrying dagger or smaller shield, those also tend to develop similar skills, though the reach and use difference significantly changes how you go about it. (Larger shield mechanics around attack and defense work very differently and don't carry over as much).
It's also worth noting that a key skill that often gets overlooked in two weapon styles is fluid transition from unarmed to armed and back again - you might start with one weapon, begin a counter, draw a second weapon and attack in one motion, get your 1st hand locked, drop the weapon to escape the grip and counter grip while your 2nd hand makes another attack. The ability to switch up quickly in response to the need of the moment makes it harder for the opponent to adapt.