As always, there will be a part 2 so stay tuned to the Bat-Channel!
You hold a nice collection:
You open 1♠, annoying LHO preempts 3♥.
In addition to the normal tools, we play that a double by partner here is 10+HCP, and pretty likely not to have 3+ cards in spades and unlikely to have a heart stopper.
Partner bids 4♣. You rebid 4♦. Partner bids 4♥. What do you think he has? What is your next bid?