Normally, peasant armies can be wiped out with few casualties on your part. I don't know how much you know about the game mechanics, but you should have a significant morale edge if your military support slider (not the research slider) is set to over 1.00 (I generally set it to about 1.10 in peacetime to save money, and max it out at 2.0 for a major war). After the first couple of military tech advances, you should be able to convert your infantry to Men at Arms, which are FAR more effective than the peasant levies you're facing now (prioritize one tech so you get it a lot sooner, rather than spread out the points and not see ANY new tech improvements for decades). If you can afford 50 ducats for a general, that might provide an additional advantage (if he has a + to melee), and with all those fights, you should have passably decent Army Tradition to get a better general than a useless 0/0/0/0 skill. Normally, if you have a couple of troops stationed on the border (in groups of 2 units, because 1 lone brigade will often get "auto-wiped") so you're the defender, not the attacker, that should give you a terrain advantage in a lot of cases. More importantly, the units from the other countries will often be driven there by being broken in combat, so if you intercept them immediately (ideally, have troops waiting for them), they may be on the verge of breaking right from the start. Waiting will help them a lot more than you.
Aquiliea has the population and province quality to have a decent income (unlike Hungary, for example), so affording the troops and generals shouldn't be an issue. Playing "Ping-Pong" with rebel units (chasing them back and forth and fighting them over and over) can be a drain on manpower, so you probably want to send enough troops into the fight to win, but keep a couple in your adjacent provinces, so the enemy will more often retreat back into the other country where they came from, or else get auto-wiped when their broken army runs into your stationary defenders and your main army shows up to reinforce.
I'm no expert in the game, but have run a handful of campaigns and know most of the major points. I don't think there's anything you can do to get rid of the Peasant War modifiers In the adjacent countries, and as long as they're fighting their own peasants, they're not sending armies to invade you. If you think you have problems with a few unruly peasants, wait until you find yourself at war with Austria when they're the HRE, an alliance of Venice and Milan, or Hungary allied with Poland. Form your own alliance with at least one bigger state; sending a few troops to assist in their wars beats finding yourself fighting alone if/when you get attacked.
