This is a tough one. Is the problem with the Civic because at least one seat is rear-facing? Two forward-facing seats plus a booster should be fine. I drove a Mazda Protege5 so outfitted for years.
The issues with the Mazda5 tend to involve the suspension--check the problems pages on the site--and possibly rust. The engine and transmission tend to be reliable. Those 2010 and up are more reliable, but also probably too expensive.
Kia offered the similarly sized Rondo for a few years. The Rondo also had 2-3-2 (with the third row optional, they don't all have one) rather than 2-2-2 seating, but it didn't handle as nimbly as the Mazda. We have just a small amount of reliability data on these. What we have suggests that the 2009 is more reliable than the 2008 which is more reliable than the 2007, which could be pretty bad. The most common engine repair appears to be ignition coils, which aren't expensive. A few owners with the V6 engine also report that the oil pan rusted out.
Among two-row vehicles, the Hyundai Elantra Touring is larger than most. It was marketed as a wagon in Europe. Reliability has been so-so, but few of the reported repairs involve the engine or transmission. Mostly minor stuff. Could be a very good fit if you can find one in your price range. Might be too new.
With larger minivans, you'll have to make a tradeoff between a newer Dodge / Chrysler and an older Honda or Toyota. The Japanese minivans probably only fall within your budget with a lot of years and/or miles.