Suppose my opponent has a Kaervek the Merciless
Whenever an opponent casts a spell, Kaervek the Merciless deals damage equal to that spell's mana value to any target.
and I have a Balefire Liege
Other red creatures you control get +1/+1. Other white creatures you control get +1/+1. Whenever you cast a red spell, Balefire Liege deals 3 damage to target player or planeswalker. Whenever you cast a white spell, you gain 3 life.
It's my turn, I have 1 life left and I try to Sword to Plowshares Kaervek. If I understand the rule correctly, I will first put the Balefire Liege +3 life on the stack, then my opponent will put the 1 damage to any target on the stack. On resolution, Kaervek will deal damage first and I will lose instantly. Rule 603.3b states:
603.3b If multiple abilities have triggered since the last time a player received priority, the abilities are placed on the stack in a two-part process. First, each player, in APNAP order, puts each triggered ability they control with a trigger condition that isn’t another ability triggering on the stack in any order they choose. (See rule 101.4.) Second, each player, in APNAP order, puts all remaining triggered abilities they control on the stack in any order they choose. Then the game once again checks for and performs state-based actions until none are performed, then abilities that triggered during this process go on the stack. This process repeats until no new state-based actions are performed and no abilities trigger. Then the appropriate player gets priority.
It makes no sense to me as the active player will always be at a disadvantage since its triggered abilities will always resolve last.
Is this the correct interpretation of the rules? Would waiting for my opponent's turn to cast the Swords to Plowshares change anything to this?