As I pointed out in my post above, I have the right to even decompile software to enable interoperability if I want.Except the first sale doctrine only deals with resale of the original copy. It has nothing to do with what we are talking about. It does not give you rights to modify the software, nor does it give developers rights to distribute modifications to the software. It certainly doesn't mean that Apple should be forced to modify it's software to support third-parties.
Directive - 2009/24 - EN - EUR-Lex
You're right that the existing Law did not require Apple to modify its software to support interoperability/third party software, but the DMA does seem to mandate that.
The fact that I own a copy of the software means that I can choose to install or create programs to interoperate with it.Again, all it means is that you can resell the original copy that you purchased and pass on the original licensing terms. Hence, the name.
There are even exemptions to the restrictions on reproducing the software with the goal of enabling interoperability:
From the above link point 15:
"It has therefore to be considered that, in these limited circumstances only, performance of the acts of reproduction and translation by or on behalf of a person having a right to use a copy of the program is legitimate and compatible with fair practice and must therefore be deemed not to require the authorisation of the rightholder. An objective of this exception is to make it possible to connect all components of a computer system, including those of different manufacturers, so that they can work together."
It should be noted that the DMA goes further than this even in requiring not only that Apple not prevent these actions to enable interoperability but that Apple actively facilitate interoperability via the way they design their software.