Yong Kai led the force, not Meng Huo. To make this explanation clear, let me point out that Yizhou Commandery is one of the dozen-ish commanderies of Yizhou province (just as New York City is physically a small part of New York State -- although NYC area has over half the state's population, while Yizhou Commandery only has a small part of Yizhou Province's population).
In 215 Liu Bei took over Yizhou province from Liu Zhang. Either Yong Kai refused to accept Liu Bei as the leader of Yizhou, or he accepted Liu Bei but rebelled a few months later. In any case, 215 also had a territorial dispute with Wu (over whether Nanjun was a gift or a loan), and Cao Cao took over Hanzhong from Zhang Lu. Both were more important than the ruler of distant Yizhou Commandery.
In 218, Gaoding rebelled, killing general Jiao Huang (who, to my knowledge, was not known for anything other than getting killed by Gaoding); the famous Li Yan (Administrator of Jianwei at the time) defeated him.
In 220, Zhang Yi [Junsi] was put in charge of Yizhou Commandery to settle things. But by then Yong Kai had been building a power base in southern Yizhou province -- so there may well have been rivaled power bases there. Again, Liu Bei was too busy dealing with Guan Yu's last days and the aftermath to directly deal with Yong Kai.
In 223, Liu Bei died. Around that time, Yong Kai defeated and captured Zhang Yi Junsi; he was sent off to Wu as a sign of allegiance. In return, Sun Quan recognized him as grand administrator of Yongchang. But Shu loyalists Lu Kai and Wang Kang refused to let Yong Kai enter, so he had to return to Yizhou commandery. So he sent Meng Huo to recruit support form others. Zhu Bao (grand administrator of Zangke commandery) and the above Gaoding joined him, bringing much of Yuexi commandery.
In 225, Zhuge Liang went south to put down Yong Kai's force. He would take the western route (Yuexi), Li Hui the central route (southern Jianwei), and Ma Zhong (not the Ma Zhong serving Wu, but Ma Zhong [Dexin]) would take the eastern route (Zangke). As for Yong Kai's force, they planned to draw Zhuge Liang into the south and cut him off from northern Yizhou province,
Shortly after Zhuge Liang's invasion, some of Gaoding's followers murdered Yong Kai. Meng Huo was picked as the force's new leader. But what of the three Shu armies?
(1) Zhuge Liang had no problem defeating Gaodong's army; Gaoding was captured and executed.
(2) Around the same time, Ma Zhong Dexin defeated Zhu Bao. They do not say whether ZHu Bao survived, nor are there any records for him afterwards, so I would not be surprised if he died in battle.
(3) Li Hui had a harder time than the other two; he was besieged by larger numbers, so he faked a surrender. His opponents let down their guard, and Li Hui crushed them in battle, then met up with Ma Zhong Dexin to the east.
By now, Meng Huo was the only remaining southern leader. He was respected by both the chinese and the non-chinese, so Zhuge Liang wanted his submission, not his death. While the historical work claims he was defeated seven times, I find that unlikely for two reasons:
(1) They give no details on the battles.
(2) They have details on when Zhuge Liang left from and returned to Chengdu down to the month. If you include travel time (about 500 miles, plus they have to set up camps, cooks, etc. every day) that only leaves about a month for seven battles with Meng Huo, each of which requires him to regroup his troops, convince them that despite losing X battles in a row they can win battle X+1, and convince them that despite losing X times in a row he's not utterly incompetent.
So I imagine there was only one, *maybe* two battles. Remember, they like to exaggerate, especially when non-chinese are involved. He Qi's biography, for example, claims that when fighting bandits in rural Yangzhou they faced a sorcerer whose spells protected from metal edges and sharp arrows -- thus causing his army to attack with wooden clubs and win easily.
In any case, to deter rebellion, Zhuge Liang put local officers in charge of the south: Meng Huo, Meng Yan (may or may not be related to Meng Huo), and Cuan Xi (an uncle of Yong Kai).
As for Wu and Wei, Cao Pi invaded three times between 222 and 223. He planned a fourth invasion in 225, and sent an army of 100,000 troops (Incident at Guangling), but when he saw Xu Sheng's dummy walls, he turned around and left without any actual fighting.