What if I set up an additional session price and a discount code, will they both be applied for a purchase?

If both are set up, then both apply.

And the additional-seat price is figured first, before the discount code. 

For example, if the class is $150, and the parent bought two seats, then the first seat will pay $150*50% = $75, the second seat should pay $150*50%-$5*50% = $75-$2.5 = $72.5. The parent will pay $2.50 less for their second seat instead of $5.