Had you split with a cash bet, you would have kept it.
Since the second bet was a free bet, you don't get to keep it. Your second bet pushes, your first hand loses. Your first hand will be with a cash bet, your second with a free bet. doubling A7 v 6), you need to do so with cash.
This means that if you want to do soft doubles in accordance with basic strategy (e.g. At the games I've seen, you can double for free on any hard total of 9, 10, and 11, and split any pair except 10-valued cards.
