The util is high (71%), is this hurting MY credit? --most likely. That's crazy high util.
Would dropping this account from my credit report hurt me more than it would help? --no telling; we don't know what else you have going on.
What's your AAoA (average age of accounts)? How old is the AU card? (opened when) What other accounts do you have? What's the util on your own cards, not counting this one? Do you have any baddies? What are the negatives listed, in order, on screen 2 of your FICO score reports?
The handy thing about AU cards is that you can come off the account, ask that it be removed from your reports, pull your scores, and see what happens. If there isn't much change, and if it makes sense for your family finances for you to use the card, you can then get back on.
I hope for your hubby's sake that there's a plan to get the balance on that card down to $0. 
Well, the card is "younger" than your AAoA, so it doesn't help you there, and of course, the util definitely hurts.
The trick will be that you will be left with only one CC. It's possible that the AU card does help by representing a second revolving tradeline, although my guess is that it's still hurting more than helping. Your scores are surprisingly low for what you listed (lates on an SL), unless those are shiny new lates.
It's definitely worth seeing what will happen. And if your scores do jump afterwards, I think it's time to get a second card in your name. Having just one CC leaves you pretty vulnerable to lender weirdness. 
