"Wouldn't application #3 claiming priority to both application #1 and #2 make the examiner aware of both co-pending applications?"
af: There is at least one CAFC "inequitable conduct" case out there in which enforceability was "saved" by such a recitation in a spec (no scienter). But IC cases are very fact specific. It's my practice (and that of other practitioners I know) to "flag" the relationship for the Examiner in my transmittal of the first IDS or other paper. Embarassed I can't remember (and too lazy to go look on Friday afternoon), but there may even be a (strong) suggetion ("should") to do this in the MPEP.
Getting back to the OP. it's an interesting question. The Office has said that the apparatus and method are independent and distinct - separately patentable inventions. In my experience, this is often just a "knee-jerk" reaction on the part of Examiners. But the Office's conclusion might indeed be given some weight in DCs (did you petition and loose? even better argument if you did).
If I recall the policies behind double patenting, one is improper temoral extension of the patent. Ur TD over method patent 1 addresses any improper temporal extension of that parent method patent. Obviousness type DP looks at the claims of the respective patents / applications. Unless a method can only be practiced with one apparatus that one apparatus and that apparatus is only good for that one process, I don't see a method claim renedering an apparatus claim obvious, or vice versa. This "policy" does not appear to be implicated. But the "safe harbor" of 119 might be (in ur favor - need to think that tru).
The other policy I recall is "vexating" or "duplicative" litigation. Again it boils-down to ur particular facts. In the chemical arts, it would not be impossible (or even uncommon), for "A" to own a process for making product P, and "B" to own an apparatus that can be used for making, inter alia, product P. An actor could infringe one or the other or both. This policy does not appear to be implicated (esp if the Office was right).
So what to do? It's really up to the client. Do they mind keeping 1, 2, and 3 together? I can imagine a big chem or pharma company not minding if it would avoid what I percieve as a very small "risk". Own all three, practice the method, and license the apparatus to a manufacturer of chem process equipment whilst retaining sufficient rights so that they (owner) would be a necessary party in an action allegeing infringement of apparatus patent 2. Any litigators care to comment?