Scalia's scribblings on Heller are, sadly, in my opinion the worst written opinion he ever sat down. He leaves ambiguous the two most fundamental questions that needed to be solved:
1) Do citizens have the right to protect themselves wherever they may be, and
2) Does the 2A protect that right wherever they find themselves
Scalia goes to great length in Heller discussing the common law and historical antecedents and references, which is all well and good, and then punted by so narrowly (and unnecessarily, in my opinion) tailoring Heller around the specifics of that particular case that any lawyer worth a nickel could use it to justify any restriction he/she wanted. Scalia was no fool - he knew what was riding on this decision and that it would be parsed seven ways to Sunday for any opening in which a gap could be exploited to shrink the fundamental 2A right, and he gave them exactly what they asked for. For God's sake, he even invented a notion of some sort of "core" 2A right as a subset of the entirety of 2A rights, basically inviting his opinion to be evaluated in this fashion.
Imagine if landmark rulings like Brown v. Board of Education were litigated in this manner. Outrageous, right? Yet Scalia knew that is exactly how his opinion would be litigated and one can only assume he deliberately wrote it in such a way as to allow it to heppen.
All he needed to do was make clear the answers to those two fundamental questions above.
It would have been nice if Heller had addressed those questions, and I agree that SCOTUS does need to address them, but the law Heller was about didn't involve defense outside the home, so it's not surprising that they weren't answered. The Supreme Court has to answer the question posed by the case they are hearing, not issue blanket policies. To quote Heller:
But since this case represents this Court’s first in-depth examination of the Second Amendment, one should not expect it to clarify the entire field.
DC v Heller, p63
Heller does refer to self defense as a core protection of the 2nd, but you're going to have to provide citations where it's defined as a subset of anything.
Blaming Scalia isn't called for; there is no limit to how far anti-gun bigots will twist any ruling they don't like to make it say something it doesn't, as recent lower court decisions have proven.