Is there any way to Full Function 4k screen share with a mac mini that doesn't involve lowering resolution?

What would be really awesome would be a screen share touchscreen setup to carry around so I could leave the mini in the HT setup and see all the icons on the handheld I'm sure there is some way this could be done but I haven't been fooling around with computers for some years now. I've been living in a very poor internet/cell connectivity area and only recently bullied the local cable internet provider to run service to the house, making a computer a worthwhile investment. Are there screen mirroring devices/apps for iPod or iPad? The problem is connectivity with the TV. Unless it is physically plugged to the mini, DRM prevents viewing iTunes content. It looks like an apple TV will help out with iTunes at least but this implementation is getting supremely expensive compared to a windows mini pc which will also output 4k 60hz and scale text and icons to be usable on the couch in the living room. I'm not trying to beat a dead horse but apple actually advertises the mini as a viable htpc device so I feel a bit letdown by my troubles. How hard can it really be to get text and icons scaled for usability on a large screen? You would think an OS update fully 5 years after the first 4k TVs hit the market might have something for us non-desk computer people. An organic extension bringing computer usage into casual everyday life should be moving this way instead of the legion of cell phone zombies stumbling around with their faces glued to their phones. I refuse to be assimilated into the collective as futile as my resistance may be!