Have you calculated how much interest this is going to save you?

It doesn’t appear to be very much savings. the $250 fee would probably wipe out the interest savings. You could just get more gazelle intense. Why not just get a personal loan from the credit union for both of the loans instead of a HELOC? Why put your house at risk for a car? I would put the extra money into the HELOC to give you room in case you need to sell the house. Are you underwater on the house?
I would not trade debt on a car for debt on a house. You have 3 years left to pay on a $10,000 car? Can you sell it and get a $5,000 car?

I remember 20% interest rates on mortgages.

We moved into our house 30 years ago this week, and closed on it March 30, 1980; paid the builder rent for 6 weeks. We had locked in the interest rate on our mortage at 12 and a quarter percent, 30 years fixed, in December for 90 days. It took 90 days to get the cash DH had saved through some program at work. The builder was willing to work with us–sure sale while still under construction versus the unknown, with interest rates rising daily. The day we closed, the fixed rate was 18 and three quarters percent on a 30 year fixed mortgage. A few years later
we refinanced to 8 and something for 15 years, and our mortgage didn’t change a penny the first year!

I like the idea of refinancing the car loan

into a lower interest loan – if you can’t sell the car – but *not* to a variable interest rate loan. Interest rates are at record lows and they are going to go up up UP at some point,. Remember that 30 years ago the Prime Rate was over 20%!!! Today’s interest rates are going to look like a screaming bargain in a few years.