I will also add that the main reason for the first war was due to Sui officials discovering Goguryeo diplomats in a Turk camp, which implied that Goguryeo was ignoring Sui's requests for submission. Although the first campaign failed in part due to adverse weather conditions, all of the other campaigns also had to be abandoned as winter set in, and the Sui forces were defeated both on land and sea, which meant that Goguryeo was thoroughly prepared. Later, during the second campaign, Goguryeo's main strategy under Eulji Mundeok during the conflict with the Sui was to lure the enemy further into Goguryeo territory, then devastate them in a decisive battle, which is what occurred in the Battle of Salsu River. Ultimately, Goguryeo's determination to remain independent, and the Sui's failure to effectively supply its troops, inability of the generals to make independent decisions, and low morale caused the campaigns to fail.
I'm not really sure about what you mean when you state how the Sui needed to attack the Turks and Goguryeo to survive. Goguryeo was more concerned about maintaining a general balance of power between the states in the area, which was why it made a preemptive attack in Shanhai Pass around 595 in order to assert its dominance over its respective region. It also sent diplomats to the Turks because it was preparing for a Sui invasion, and neither Goguryeo nor the Turks probably thought about attacking China.
If another Sui successor decided to attack Goguryeo by utilizing more effective strategies, it would still have been hard for him to be more successful than Taizong of Tang, who was initially successful because the Goguryeo generals who initially clashed with him on his way to Ansi Fortress failed to comprehend the Tang's strategy. However, he failed to realize that there were numerous Khitan and Mohe tribes, which meant that although some sided with him, the others had been allied with Goguryeo for decades and did not have a reason to aid the Tang. In addition, his deliberations before approaching Ansi and his failure to take it illustrates how although he might have taken more fortresses if he had utilized a different strategy, he would eventually have been bogged down after losing contact with supplies or guerilla warfare deep in Goguryeo territory.
As a result, although it's unlikely, if the Sui had acknowledged Goguryeo dominance in Northeastern Asia, both states might have lasted for at least several decades or centuries longer than in OTL.