In a similar boat to the OP. Son was just born, child seats are huge, and with the stroller in the trunk of the GTI with the diaper bag there's literally no room for anything else. Need something bigger, still fun to drive, and decently priced.
I still haven't moved on anything yet, but I did go drive a Kia Stinger GT2 and absolutely loved it. You might be able to find them lightly used in your price range (I'm Canadian so our market is a little different). It's a sportback like the A5 (similar in overall size, too) and the usable trunk space is enormous and easy to access. Auto-lift rear hatch should be a lifesaver with balancing kid/groceries/etc. The car is FAST, and hugely fun to drive. Obviously AWD and bigger, so not the chuckable nature of the GTI, but gobs of torque and as quick as a Golf R from a dig. Interior is spacious and very nice, tons of amenities, great seats, great audio, and a great looking car IMO. Very long warranty as well. It's a KIA, I get it, but they're easy to de/re-badge if it bothers you.
Go drive one. You might be as surprised as I was. Seriously considering it.