The point of mentioning half-elves was just to show that there would be adjustments such as adding a +1 here or there just like with half-elves.
I actually feel rather silly as I realized after I asked the question I had never actually searched under the terms "half dwarf" and what I found when I did was actually very eye-opening and went right along with my own thoughts on why you might want to play such a race.
First of all, AD&D 3.5e has half-dwarves as playable races! Check it out: http://www.dandwiki.com/wiki/Half-Dwarf_(3.5e_Race)
And if you're up for a laugh, check out this Reddit discussion: http://www.reddit.com/r/rpg/comments/182pse/why_are_there_no_halfdwarves/
When all is said and done it looks like this is actually something that could be added to Pathfinder and could be a lot of fun to play with! I personally usually end up running the games we play because no one else in our group seems to have any organizational skills. But if I wasn't running it I'd love to play a half dwarf!
Anyway, I kind of answered my own question, except for where the name "sunderkin" came from in the first place. Sounds like a pretty legit kind of name to me. I think I'll try incorporating this new class into my next campaign - I'm taking the group into the Emerald Spire. And I just picked up a copy of Pathfinder Unchained so that should be helpful in fleshing out the details of this class.
Still, I'd love to hear more from the community. What would be pros and cons of this kind of a class? Would anyone want to actually play one? I know I would but apparently I'm biased!