I'm trying to recreate a has_many :through
relationship inside my extension. Is there something similar that I can use in TCA?
TYPO3 has MM-relations with full handling, but what you want looks like qualified MM-relations.
This has not been implemented yet in TYPO3.
So you need to realize it by your own: have three models where one model has n:1 relations to the other two. All handling, like selections, needs to be done in your code.