Additionally, if they could / did, how did the emperor resolve this issue?
Well, the different estates of the Holy Roman Empire did duke it out to settle their differences, and this is actually the thing that the Holy Roman Emperors Charles IV and Maximilian I wanted to end in their Imperial Reforms.
Before Charles and Max, essentially, duchies, counties and even the Kingdom of Bohemia participated in wars against one another, like the Wars of the Swiss Confederation, the disputes of the double elections, etc. Charles IV wanted to end all the chaos by instituting the Golden Bull of 1356, which essentially said that the election for the title of Emperor was to be decided by vote, and there would be 7 electors, while relegating all other duchies, counties and other imperial vassals as second-rate vassals.
Maximilian, meanwhile, instituted the Reichskammergericht, or the Imperial Chamber Court, where all disputes should theoretically be settled in court, but in practice, this was mostly not followed and applied only to the lesser nobility having feuds all over the place.
In a practical sense, if the Holy Roman Emperor wanted peace in the land, he either needs to mediate between the warring parties to essentially forge a peace treaty or he needs to beat everyone to submission, something that did not work out well to Austria's favor during the Wars of Religion.