Kids shuffling cards
JavaScript (ES6), 192 188 185 bytes



document.write('&lt;pre id=o&gt;')
s='ABCDEFGHIJQRSTUVWXYZ'
a=[0,...123456789+s.toLowerCase()+s]
setInterval('o.innerText=a.join``;a.splice(Math.random(s^=1)*48+1,0,s?a.pop():a.shift())',250)




Edit: Saved 4 bytes thanks to @L.Serné. Saved 3 bytes thanks to @Arnauld.