Oh, it sounds like you have Gavelkind. Which, if you're trying to build a large empire, is not so "kind". Under Gavelkind, the realm is divided among the sons (or daughters, if there are no sons and succession is agnatic-cognatic), with the eldest receiving the primary title, the second-oldest the secondary title, etc., and down on the list. So your eldest son received the County of Tir Chonaill, and the second received Tir Eoghain.
So what can you do? If both counties had been under a Duchy you controlled, the eldest would have received the Duchy and the primary County, and the younger would've controlled the county, but still been a vassal under the older. However, establishing a Duchy in one realm can be challenging.
It's for this reason that a lot of players prefer other succession options. Primogeniture (oldest inherits everything) is often preferred, but Ultimogeniture (youngest inherits everything) and Seniority (oldest family member inherits everything) are easier to implement. There's also Elective, where the candidate with the most votes inherits the title, but IIRC that's only at Kingdom-level and above.
I see you are getting the hang of political intrigue and treachery, though.