Hi Stubble --
The things you say you need the money for, buying a car and finishing a basement, aren't really things you need. I think they're things that will be nice to have, but really, you don't need to finish a basement or have a nice new van if you have kids. Lots and lots of kids have survived just fine in the large house you describe already having, and lots of kids get from point a to b without a minivan.
So I would treat this money differently from an emergency fund. If it were emergency money, sure, I'd keep it in cash. Not much return but no risk other than inflation. But what would happen if you did invest this, and the stock market tanked? Well, for a short period of time, you would seem like you had less cash. But in reality, what you bought would be exactly the same thing, unless you needed to sell it (1000 shares of X is still 1000 shares of X, even if its value changes). Let's say another 2008 happened. The market is back, only 6 years later, with a vengeance. So if you can hold the stock (ie, live without a mancave in the basement or 7 seat minivan for awhile), you'd be fine in the long run, right? Given a market that behaves as it has historically.
I like the idea of paying down your mortgage as well. If you have more equity, you could always take a home improvement loan when the time came for the basement, if needed. Until then, you'd have less, or no, debt.
Good luck!