Official Riftbound ruling
What happens when I play Hostile Takeover gaining control of my opponent’s ready unit, move it to base, and then play Temporal Breach choosing it? Where will the unit go?
The unit will remain in Banishment.
Units cannot be played to a base of a player other than their own controller under any circumstances. Because the owner of the unit is the one being instructed to play the unit, and the location they are being instructed to play it to is a base other than their own, it isn’t possible to play the unit. During the check legality step of finalization, the unit will be returned to banishment from the chain and all actions taken will be undone.
Riot's question and answer, word for word, from theVendetta Rules FAQ and Clarifications
The cards
Hostile TakeoverSpell
Hidden (Hide now for
Any Rune to react with later for 
0 Energy.)Take control of an enemy unit at a battlefield. Ready it. (Start a combat if other enemies are there. Otherwise, conquer.)
Lose control of that unit and recall it at end of turn. (Send it to base. This isn't a move.)
Temporal BreachSpell
Hidden (Hide now for
Any Rune to react with later for 0 Energy.)Banish a unit, then its owner plays it to the same location, ignoring its cost.