This is valid by the rules, but might get called out as metagaming
As Token's answer adequately covers, what you've described is valid according to the rules for readying a spell. However, depending on the style of play used at your table, your DM may disallow it because it is metagaming; that is, having your character act based on out-of-character knowledge. Here's what the rules have to say about rounds and turns in combat (emphasis added):
A typical combat encounter is a clash between two sides, a flurry of weapon swings, feints, parries, footwork, and spellcasting. The game organizes the chaos of combat into a cycle of rounds and turns. A round represents about 6 seconds in the game world. During a round, each participant in a battle takes a turn. The order of turns is determined at the beginning of a combat encounter, when everyone rolls initiative. Once everyone has taken a turn, the fight continues to the next round if neither side has defeated the other.
Note the sentence I have highlighted in bold: within the fiction, characters in the battle aren't really taking turns. They're all fighting simultaneously and continuously, but because simulating real-time combat is not practical, we compromise realism in favor of simplicity and have them all take turns in initiative order. However, this means that the initiative order is part of the game, not part of the game world, and thus the initiative order of combat is out-of-character knowledge, which means using that knowledge to guide your character's actions constitutes metagaming.
So, if you attempt to use this "double-spell combo" at a table that values in-character role playing and frowns on metagaming, you will probably be called out for choosing a trigger condition that has nothing to do with your readied action. You are effectively trying to find a loophole that lets you specify "after the target's turn ends" as your trigger in order to deny the target an end-of-turn save. On the other hand, other tables are happy to embrace the turn-based gameplay and treat combat like a game instead of a simulation, and they will instead congratulate you on the neat trick you found. You probably already have a pretty good idea of which kind of table you're playing at, but if not, you should ask your DM ahead of time before you try to pull out this trick during a session.