responsive/mobile look

I’ve been having issues with the whole responsive layout business! If I configure jetpack ‘mobile theme’ widget my site looks really bad on a smartphone, its got the blue border and the theme doesn’t show, it’s a generic template by the looks of it. When I deactivate it the site looks like it does on the computer but obviously difficult to navigate because of it’s made for big screens. My site is https://www.britpakgirl.com , I came across another site which runs the same theme and looks like how I want mine to look like on a mobile, that’s https://www.whiskgirl.com ! Please help. Thanks