3rd party shop / checkout / scheduling integration

I need a customer to see the full price, only have to pay 50% of said full price (not just tack a 50% discount on, sometimes I run promos at varying discounts and they need to still be able to see the promo price and still only pay 50% down at checkout). Upon checkout / payment confirmation, I need my customers redirected to acuity or another 3rd party calendar app so they can book a session. Ideally, based on the criteria they select at checkout, I'd like for my site to estimate the amount of time needed and then block out that number of hours or days on the calendar when they book their time. 

I know, a tall order, but it would really streamline client experience. Any way to go about this?

Did you ever find a solution @sosiaben

This sounds exactly what I'm trying to do. Any luck @sosiaben ?
Thanks