So it looks like the main problem with this is the use of Sets. It seems like you don't need the sets you use for what you're trying to do - you can just use the fields as-is. I really only use sets if I want to filter on a combination of multiple Dimensions (like all combinations of grade_level and Subgroup), and don't use it for single Dimensions like you have here. If you see the attached, both the "data new" and "view new" sheets have the data the way it seems like you need, but I'm not using any sets.
On the other side of things, I'm not sure exactly how your original data is set up and what the data is showing, but I'd guess you'd also need to join on Year. I created sheet "potential data issues" to show you what's going on. Each of these is a row in your joined data source, and you can see if you don't join on year, it repeats each row 3x, one for every combination of Year in Sheet1 and Year in Sheet2. Depending on what you're trying to do, this could create a lot of issues in calculations down the line. It also makes your data source 3x the size of what it needs to be, so by joining on year you also save space, which is always nice
But hopefully this helps, please let me know if this doesn't fully solve your issue or you have other questions with this data set!
P.S. You say "If the issue is I need the two different databases to recognize the same years, how do I get that to happen?" - what type of databases does your data come from? You might be OK as is, since if I view the underlying data the two fields look like this:
YEAR year 1/1/2010 1/1/2012 1/1/2010 1/1/2011 1/1/2010 1/1/2010 1/1/2010 1/1/2012 1/1/2010 1/1/2011 1/1/2010 1/1/2010 1/1/2010 1/1/2012
Otherwise, every database is different in what the answer is....