We are already deeply engrained within Yemen with numerous military bases (likely permanent) and control of numerous Yemeni islands as well as all the areas where most of Yemen's resources are located. Deep ties with the tribes of Hadhramaut and most of Yemen.
Yemen cannot function as a successful state without KSA. Due to geography, shared ancient history, language, culture, ethnicity, religion and close tribal and clan ties this will always be the case.
The STC, which KSA also has ties to and with many powerful individuals within being directly allied with KSA, is just a pro-South Yemen independence group in terms of ideology. They want to rule their own fiefdom outside of Sana'a control, currently occupied by the Houthi cult. After all they control all the main resources of Yemen and most of the strategic coastline of the country.
Which ironically will only lead to the fragmentation of Yemen and I personally predict that it is very likely for South Yemen and Hadhramaut and Al-Mahra province to be swallowed up by KSA eventually. Which would suit KSA very well and give us a direct access to the Arabian Sea and wider Indian Ocean.
In fact many people of Hadhramaut and Al-Mahra want to join KSA and have pledged for help in this endeavor.
Personally I am all for implementing steps that foster the integration and unity of Arabia.
Anyway KSA and UAE will find a compromise that will satisfy both parties and due to geography and the other reasons I gave earlier, KSA will always be the most influential country in regard to Yemen and all of the Arabian Peninsula and vicinity.
Even more so given the impressive economic, industrial, scientific, demographical, military etc. rise of KSA.