Altough I quite like the current vassal system with the tribute that has to be paid each round, I think it could be a bit deeper.a good refference for the new vassal system would be Hoi4 together for victory, in which the vassals have different levels of autonomy from their master.
Example levels for aoc2:
-Dominion: able to call vassals into wars, but they can deny the request. and a samll tribute would be paid
-puppet/satellite: vassal is forced to join the master's war. the master is able to build farms,workshops etc. in pupptets territory and a larger tribute would be paid.
-integrated puppet: vassal is forced to join the master's war. the master is able to build farms,workshops etc. in pupptets territory and a great tribute would be paid.
the master can also controll the puppets army and is also able to disband them.
changing their levels of autonomy could work in two ways
1. the master can spend gold in order to slowly reduce the autonomy level of the vassal similar to hoi4 with autonomy bars. the vassal could gain autonomy by spending gold or helping the master in wars.
2. the master can spend gold and the autonomy would be instantly reduced and the vassal would need to help in wars to increase their level.
The already established liberty desire of vassals could also be used for the new system.
the liberty desire would show the increase of autonomy per round examples would be:
10% liberty desire = 0.1 point increase of autonomy per round
30% liberty desire = 0.3 point increase of autonomy per round
50% liberty desire = 0.5 point increase of autonomy per round
100% liberty desire = 1.0 point increase of autonomy per round
this is just a suggestion and you could comment what you'd like to improve.