I've been driving a Matrix since my son was born. We're getting ready to add a second carseat to it and wondered if we should upgrade to something bigger - but after looking at EVERY car Toyota had on the lot (yes, we love Toyota too), nothing gave us so much more space without being HUGE that would be good enough to give up our amazing mileage.
I know I can fit two carseats in the back, easily (one on either side), and thankfully my son will be in a toddler seat not long after the baby gets here, which will clear up room for an adult to also sit in the back.
The hatch area really is large - as long as you have two well behaved dogs in the back, I'm sure you'll be fine. My big dog is not so well behaved in the car, and while he has lots of room to scramble and play back there, he uses it all! If he were just sitting still, there'd be plenty of room for another. The back is fully plastic if you remove the floor mat on the bottom - roll it up and put it somewhere else and it's dogsafe!
I couldn't justify a minivan when I'm not toting around more kids. I'm not a soccer mom (yet), my son is only 3! I don't need the HUGE vehicle, and the Matrix really does have a LOT of room in it for being a compact car. If you have any doubts, many lots will let you 'borrow' a car to drive home, or around in - go ahead and put two carseats in it and put the dogs in for a moment.
Basically, I absolutely love this car. My only complaint is that because we bought used, we didn't get a 4x4!
By the way, when carseats are not involved, we can pretty comfortably fit three adults in the back, one of which is my very tall and broad brother of 6'6". My husband (at 6'2") has plenty of headroom when driving with a cowboy hat, but when I'm driving alone, I don't feel like I'm driving a big echoey box, which is how I felt when driving both a Highlander and Rav (though less so in the Rav). IF we were to upgrade, it would be to a Rav. It's the next economical choice for us, can have third row seating if chosen, and isn't (too) huge... it's actually narrower than the Avalon.
GOOD LUCK with whatever you choose - it's awful having a car that doesn't fit your needs!