You won't get a better rate than the one the credit union gives you, not with your current score.
To the person who got a better rate by putting 7k down, you really didn't....they used some of your money to buy the rate down, which means basically you paid some of the interest they were going to charge you up front, so it now looks like you have a lower rate. You may have save a bit of money, but it isn't the same as if they just gave you that rate with no money down.
As far as real estate loans vs. auto loans and the preferred rates, they are basically the same criteria. I just refinanced, and to get the best rate the minimum score was a 660. I'm sure that varies by lender a bit, but as far as used car rates go, we've had some very low rates offered by a couple of banks, but they had a 720 minimum score requirement. I haven't seen any mortgage rates that required a score that high, but I wouldn't be surprised if there were some.
If you are buying a new car and trying to get the 0 percent rates that are going around, you can get away with a score lower than 700, usually. Again, varies by dealer/manufacturer.
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