We've had a couple of our cats do the heat thing over the years. The last one was Mrg, and from the time she was over her heat session to the time of the surgery was less than 36 hours, which caused some issues for quite a long time. We found out from another vet that ideally surgery should be at least 10 to 14 days after a heat session. If that helps you with making your appointment for the spaying. Something for you to think about.
Let us know how Lily and the new puppy do.
I can sympathize with your hubby over the shenanigans the cat goes through when in heat.