Two suggestions, get an Estwing 26 inch camper's axe. Medium size between a felling axe and a hatchet and pretty much indestructible. https://www.homedepot.com/p/Estwing-26-in-Camper-s-Nylon-Vinyl-Grip-Handle-Axe-E45A/100351735Or get a Pulaski axe /tool. https://barebonesliving.com/products/pulaski-axehttps://www.homedepot.com/p/Husky-4-0-lb-Landscape-Axe-with-34-in-Fiberglass-Handle-HD-F500LS/206768935?MERCH=REC-_-searchViewed-_-NA-_-206768935-_-N
Obviously I'm partial to something like this:https://www.firefighteraxe.com/product/pickhead-axe/We cut windshields with them using short strikes to the glass in order to chop a line along the bottom and top. Pick head had multiple uses. With all the use/abuse I never saw a handle or head break.
That looks like a terrific axe. I was thinking, what about a Tomahawk? It might make a good car/truck companion being able to remove the head from shaft?
Hm, if cleaning brush is the main function, why an axe? Why not use something that was actually designed for cleaning brush, like a machete? I keep a Tramontina machete in my trunk for just that purpose. It easily cuts even through thicker branches. https://www.tramontina.com.br/en/p/26600016-262-tramontina-16-machete-with-carbon-steel-blade-and-black-polypropylene-handle
I’ve got Estwing Camper’s Axes in vehicles myself.