Firstly, you're confusing two separate historical events. I assume that what you're refering to as "their king marrying the Polish queen during Poland's interregnum" is  when in 1385 Jogalia (who was the Grand Duke of Lithuania, not the king) married Jadwiga of Poland (who actually held the title of king, not queen, so de facto there was no interregnum). The second event being the Union of Lublin, in 1569 which is the factual beggining of the PLC.

It's a bit more complicated than this, but Poland and Lithuania were more or less connected by a personal union between those events, which changed into o real union in 1569. When a ruler held both titles (King of Poland and Grand Duke of Lithuania) they would use the "more significant" one as their "main title", (also, your statement that anyone could give themself the title of king is incorrect) thus IMO it's more accurate to say that the Jagiellonian dynasty (started with Jogalia after he took the name Władysław II Jagiełło) was more of a polish dynasty that began as an offshoot of the lithuanian Gediminid dynasty, than a lithuanian dynasty that ruled Poland.

When the real union began in 1569 Lithuania had only been a christian state for less than 200 years, as they only became christened after the Union of Krewo in 1385, and before that as a pagan state (i don't like the term "pagan" but it's a good shortcut in this context) almost any political relations with christian Europe would be for them practically non existent. So by 1569 Lithuania's political power would still be quite insignificant when compared to Poland, who not only was christian for much longer, but also had established a much more significant presence in european politics.

I hope this answered your question to your satisfaction. I'm not formally educated in history so it's quite possible that i made mistakes, if so i'd be glad if someone more knowledgable corrected me. I'll post my sources later.

Your assumption that Lithuania was a stronger partner in union is simply wrong. Lithuania was already in XIV century overextended empire which coudln't face all of its neighbours alone and needed help from ally, and Poland was actually the best candidate. Both countries did not have any conflicting interests, except of the minor conflict over Volhynia and Podolia, but had some common enemies - Teutonic Order in the first place. After defeating the Teutonic Orderd in 1411 and 1466 Lithuania was actually looking for any opportunity loose the alliance a bit, but actually was more and more depended on aid from Poland in their ongoing wars with Russia mainly but also in rivalary with other baltic powers in First Northern War and constant Tatar threat on the south. For example in years 1493-1503 Lithuania lost almost half of its territory to Moscow after two wars when they were fighting alone, without any substantial polish aid. This fact only proved that Lithuania is defensless without Poland and polish lord did not want to send any more help without strengthening the union. All of this effected in Union of Lublin 1569 and actually tipped the scales for the next hundred years