>Outside they blow away because of the wide brim.
Easiest way to fix this is to fit the hat to your head like they used to do in the way back whens. This technique works for felt hats and straw hats. When your hat is new it is unlikely to fit your head well since head shapes differ so widely. A old cowboy method of fitting the hat to the head will work perfectly every time. Wet the hat and the sweat band and put it on your head until the band has shaped to fit your head with no pressure points so that it contacts all the way around your head. Then just wear it until it dries. It will always fit your head perfectly and will not blow off in the wind. You can do the same thing with ill-fitting boots. Just get them wet, slip them on and walk around wearing them till they dry. They will fit your feet like a glove.
I'm with you on the headrest thing. That's the main reason I no longer wear a hat when I drive. You have to remove the headrest for that to be practical. Years ago before headrests in pickups were a thing I wore a hat everywhere. For a while I got around it by rolling the back of the brim up so it curled enough to fit with a headrest but that defeats the purpose of the brim.
I can see 8-9 cowboy hats right now from where I'm sitting. They each fit a specific person in my family. That's one of the reasons behind it being really bad form for someone to grab your hat and shove it on their head, the hat is fit for an individual and though it may look nice on them, it won't fit - plus it's disrespectful to mess with a man's hat.
Way back in my own way back whens, I boarded my horse with an old cowboy who told stories of his younger days rodeoing and riding. At one time he held the calf-roping record time he set at Madison Square Garden. Him and some of his cowboy friends, his sidekicks, were wranglers in the 40's and 50's for movie studios in California. He had worked with Tom Mix, Gene Autry, and others and taught the lead character from Rawhide (can't remember his name) to mount and ride a horse since he had never been on one when he got the part. He wrangled their herd for that old show. Anyway, getting long here but he told me a story one time about one of the stars he had worked with who couldn't or wouldn't wear a hat, saying that he had a head too much like a nickle watermelon and a hat just wouldn't stay on it.
I was reminded of that by your comment about losing your hat in the wind. Hope this helps someone.