If I had my druthers, I would have gotten an Ody... a few months ago would have added the Sienna, but I just cannot buy a new Toyota right now. I tried
But, they were a bit out of my price range, though it sounds like they're in yours. I've never known anyone to have problems with a Honda, and I lived/work in a community with MANY MANY Hondas. (Seriously 2/3 of the vehicles around here, due to community ties.) I would say your friend's experience is the exception, not the norm.
If I only had two kids to transport, and didn't have plans for needing a 3rd row vehicle, I wouldn't get one. I would go with a larger sedan, or maybe a small SUV (with better mpg,) if you wanted something larger. Mazda5, even?
SUV-wise, I really really loved the Saturn Outlook. You can get a 2007 for under $20k. Under 15, you're looking at things slightly older/higher mileage if you want a larger vehicle, but I'm sure you knew that.
Are there reasons you want something larger than a sedan? Passenger space vs. cargo space makes for different recommendations. I ended up with an 8 psgr Pilot in which I cannot get the kids plus the cargo (my Graco single stroller only fits with one of the back seats folded down.) Good thing we hardly ever use it, lol.
And, I would just like to say I feel your pain on a tiny garage. We switched garages at my complex, and they ended up giving us a smaller new one... with all of the "stuff" we have in there (garage in lieu of renting a storage unit,) I literally had to bump my bicycle with my van to get it parked. I would park, get out, check the back, move it forward if necessary, lol. We haven't tried my new vehicle in there yet, but I hope it fits better, lol.