stump buckets can be from cheap to costly based on quality of build and brand name, there all over places like ebay, Craigslist, amazon and the web if you do a simple search
as for mounting a smaller bucket in a bigger one, I never seen anyone for sale , but gather if one really wanted to they could, but I don;t see it being a great idea, or way to spend $$
As if your going to fab something up, maybe just get a smaller bucket, , or if your trying to sort material, separate rocks from dirt
they actually sell, attachments made to do this for skid steer! from more simple rock buckets, to more costly vibrating soil separator and such, for screening top soil from dirt and rocks and debris!
if you only need things for short periods of time, many rental shops carry a good selection of attachments these days, allowing you to just rent use and return it!
also a good way to see if you like something before buying or building it!,