Honestly, you might.
Has the dog been seen by a vet? I had one once who bit with no warning and no aggravation. If there was a certain kind of motion, he nailed it - that was all.
He had a brain tumor. I had to have him put down.
It’s unlikely, but look into it.
IF you decide to take this dog (notice the really big IF) My first step would be roadwork. Find a nice, deserted stretch of road, go out about 5 AM and arrange yourselves so that you are in the car in the driver’s seat and holding onto the dog’s leash out the window - 18 inches of leash, MAX.
Very slowly ease off the brakes and coast.
The dog will quickly figure out to walk, then trot alongside.
The dog is in total control of your speed. If the leash is straight out, the dog is happy, if he’s pulling ahead, go faster, never, ever let him lag behind, slow down for him instantly.
If he is tired and wanting to stop, then stop, hop him into the backseat and go home.
Once dogs figure this game out, I have yet to meet one that wasn’t BLISSFULLY happy about this. And you will find that dogs will delightedly take far more exercise then people think. I will always remember the coonhound who figured out that even on leash he could run as far and as fast as he wanted, and went over a mile at a 21mph gallop before settling down and trotting another 3 miles at 16mph (having the speedometer is fun, dogs are fast) before even beginning to slow down.
Happy, happy dog - who went home and slept, inside the house, instead of tearing it up (and until you’ve seen 90+ pounds of coonhound shred a house you have NO idea!)
First health, then exercise, next, supervision.
Take off the dog’s collar, and run the collar through the hand loop of a leash, then buckle the collar back on - the leash is now permanently attached.
Take the snap, and keep it snapped to your belt loop 24/7. If the dog is not attached to you (or hubby), it is in a crate.
Everyone always asks when they can take it off.
A year.
Minimum.
If this seems like a lot of work, well, it is.
And if it too much work for you, sweetie, that’s fine.
What you need to ask yourself is NOT if you’re justified in putting this dog down, this dog who has bitten people. What you need to ask yourself is if you’d put down a happy, sweet, mellow dog who only wants to please you, but is black. Or short-haired. Or too big. Or bully looking. Because I can promise you one is being put to sleep even as I type this, at some shelter driving distance from you.
And if you decide to go save that dog instead - don’t let ANYONE make you feel bad about it. They’re just as free to adopt Cujo as you are.