This will not work; Readying an Action to Cast a spell requires the use of Concentration
When you ready a spell, you cast it as normal but hold its energy, which you release with your reaction when the trigger occurs. To be readied, a spell must have a casting time of 1 action, and holding onto the spell's magic requires concentration (explained in chapter 10). If your concentration is broken, the spell dissipates without taking effect. For example, if you are concentrating on the web spell and ready magic missile, your web spell ends, and if you take damage before you release magic missile with your reaction, your concentration might be broken.
—Actions in Combat, Player's Handbook, pg. 193
Unfortunately, Spirit Guardians is a spell that requires the user to maintain concentration. So if you tried to use this sequence of events, Spirit Guardians would end the moment you tried to Ready the Thorn Whip spell.
"Okay, but what if Thorn Whip was a Reaction spell that wouldn't interrupt Concentration?"
For the sake of argument, let's assume that Thorn Whip instead had a Casting Time of "Reaction, used when a target runs away from you". This would mean that we would no longer have to use the Ready action to prepare it, which means no longer needing to maintain concentration on Thorn Whip, meaning no longer breaking concentration on Spirit Guardians.
In this case, you would be able to trigger the second source of damage: this is the first time this turn that the creature has entered the Spirit Guardians' radius; previously, the creature started its turn within the radius, but it did not enter during its turn. So using Thorn Whip in this manner would deal the second source of damage that turn.
You're overcomplicating this
You don't need to bother with trying to ready an action. The effect of Spirit Guardians, in addition to dealing damage, is to slow movement of creatures affected by half. Most hostile creatures have a movement speed of 30-35 feet per round, which means that at half speed, a creature running directly out of the Spirit Guardians probably doesn't get more than 5-10 feet away from the edge of the AOE. As a result, using Thorn Whip on your own turn, as a regular Action, instead of trying to ready+Reaction it, is perfectly usable to pull them back inside the Spirit Guardians, triggering the extra damage. And if they're more than 25 feet away from you (meaning Thorn Whip cannot pull them inside the AOE), you can just move a few feet closer before casting it. This will cause them to take damage from being moved within the radius, and then take damage again when their turn starts.
So overall, this method deals the same amount of damage as the method you're trying to employ, but it doesn't require you to use your Reaction, it doesn't require you to invent a fake spell that is "Thorn Whip, but cast as a Reaction", and it is easier to make sense of in the rules of the game.