Writing to a reviewer to inform that one is not journal shopping?
I'll start with some remarks on the past events:

“the re-submission date was 10 days after I received the reviews” — If the reviewers had asked for large modifications, I am convinced you could have asked the editor to allow you more time to resubmit the manuscript (unless it was for a special issue).

“senior management […] forced me to resubmit to the same journal as is” — This is very wrong, and you should have said no (backed up with strong arguments, of course). Resubmitting the same manuscript, unmodified, to the same journal, is ethically borderline. Depending on the exact requirements for submission of the journal, and the information you gave to the editor, it may even be unethical (many journals ask “has this manuscript previously been submitted to this journal?” — if you say yes, the unmodified paper will be flat out rejected, if you say no, you are lying).


Now, regarding your questions:

“Should I ask […] the reasons for rejection?” — You can. I am guessing that the editor somehow didn't realize that it was a resubmission, if it took 2 months for it to get rejected. Thus, you probably got some new referee comments. However, if the editor didn't tell you… maybe the reviewers just flat out recommended rejection, with no comments.

“Should I explain him that I was not journal shopping and the situation was such that I had to resubmit the paper?” — I don't think so, and certainly not in these terms. There is not “situation such that I had to resubmit”: you resubmitted, and the blame of that bad decision lies with you. Pressure explains it, but it doesn't justify it.
If you want to contact the editor, I would do it very differently. Simply apologize to him for the bad decision, explain that it was done under pressure from your organization and you realized only afterwards that it was wrong. Say that you hope it won't be held against you in the future.

“I have now incorporated the suggested changes […] Should I now resubmit it to the same journal?” — I don't see why not… just make sure you carefully explain all the changes made in response to the reviewers, as a regular resubmission, and explain your earlier resubmission (apologize!).


To be honest, I don't think it will leave a bad stain to your name in the future: everybody makes mistakes, especially young researchers who don't yet understand fully the rules. Being honest and upfront in your future interactions with the editor should lead him to form a good opinion of you.