Sounds an awful lot like Germany in the 1500s. Bunches of mercenaries running around, lords that can't raise their own troops, mercenary captians being wildly rich. So a history book or two about Landsknecht (the term for these mercenary pike and shot units) and Germany at the time will serve you well. There's a couple things to remember:
1: Money doesn't buy everything. In a medieval setting, money is only sorta-useful. Sure it'll buy lots of fancy things, but when the famine comes a thousand gold coins aren't going to feed you. At the time real value (and by extension, power) comes from LAND. Specifically farm able land. Sure your mercs could conquer that land, but if nobody farms it THEY would have to, and if you're farming you ain't training and somebody else could kill you and take all your stuff! So your mercenaries are stuck being at the mercy of whatever ruling body is around because they don't have the resources/wherewithal/desire to actually control land to raise crops to feed themselves.
2: Belief is Greater than Gold. The reason mercenary armies aren't a thing anymore is that, historically, mercenary armies aren't actually all that great. They have low moral, they change sides based on who pays more, they'll not show up to fight/not fight in near-hopeless situations... the list goes on and on. So yeah you have mercenaries fighting your battles for you. But the second that army of mercenaries looks at an opposing force that outnumbers them 3:1, or you ask part of it to perform a sacrificial holding action, or three OTHER countries band together to offer the mercenary companies a literal ton of gold to not even switch sides but just sit out a battle/war, things are gonna go to pieces. A trained professional or even volunteer/mass-conscript army will beat your mercenaries. Or get in a situation where the mercs feel "talking" is better than fighting.
Now your mercenaries have been doing this sorta thing for centuries, and might end up being more like Rome's Imperial Guard and be de-facto power brokers for the nation and thus want the nation itself to survive. They might even have a loyalty to the country above and beyond loyalty to their mercenary company that'll mean they fight invaders to the last man and essentially for free. But in that case they're not true "mercenaries" in the historical sense, you've got something else going on.
My best guess is that your original mercenaries are now more-or-less the armed forces of the nation, either as a feudal aristocracy or a as a ruling/military cast, and aren't real mercenaries at all at this point. Your founding story is more myth than reality, and they work just like any other kingdom's armed forces. If they are not, then the above problems will likely lead to your kingdom's imminent demise.