Explorer seems like serious overkill for two kids. I've been schlepping mine around in a 99 Accord or my husband's 2008 Fit. We did have a CRV for a while, which got decent gas mileage for what it was, but it felt like overkill for us (so for a while we just had the Accord, and we might sell it in the foreseeable future and just share the Fit).
I agree that you probably want a car at this phase. Even the author of the book Walkable City was thinking of buying a car when he had two car seats! However, I will say that I find it much easier to strap my kids into the bike trailer than into their car seats, so I do that whenever possible :-).