The average baby at birth is what, about 20" long? Even the smallest of car seats that would only fit a newborn rear facing would be 30" in depth. Do you have 30" between the driver's seat back and the back seat? Now remember that kids grow. If your 3yr old doesn't fit behind your seat, then a second kid of yours won't when they turn 3. So in any situation, you're looking at replacing your BRZ in less than 3 years.
If another vehicle isn't in the cards, then selling the BRZ will have to be. Again, unless you are short enough to fit a kid behind your seat - be it age 3 or 6. (Rear facing infant seats take up much more space than an older kid in a booster.) Some people on this forum ARE short enough to fit someone behind them. If you're not one of those people however, you have to realize you have the wrong car for your very important needs.
As a possible way to keep the BRZ close, assuming your wife has a sedan or vehicle with decent space in back, who ever is ferrying the kids that day takes the sedan while the other person takes the BRZ. If you each need to take a kid, you're all set as the BRZ will fit one kid fine in the rear passenger side.
If this isn't a solution, then no amount of magic tiny baby seats will help you long term (ie more than a month!). The baby will grow. Your 3yr old will grow. Best solution is to have a car that will support your family's needs for the foreseeable future. Trading the BRZ for a new WRX buys you 7-10 years of time (at which point vehicle mileage, not space, might determine need for a replacement). The WRX will still be fun and sporty and will do 0-60 in 5.2 seconds. If you don't want a WRX, get a new/used Mazda 6 or whatever - I don't care. Just suggested the WRX as a way to still drive a performance vehicle.
Btw, one of the most compact infant seat on the market I can find is the Combi Coccoro - but it's not a carry/base setup.
http://www.combiusa.com/mobile/Produ...oductCode=8220