Should I add a non-requested work to my major revision of a scientific journal paper?

As somebody in a different area of computer science, I find it hard to see how including a little more true, relevant information could possibly be harmful. The reviewers think your paper is worth publishing with revisions. The worst case I can see is that, when you submit the revised version with this extra unsolicited material, the referees ask you to remove it again.

You can always mention your parent's opinion to your co-authors and see what they think.

I would want to answer this based on my recent published collaborative work on a research paper.

We were in a similar situation where one reviewer was not convinced with experimental evaluation. However, I along with my collaborators came up with an idea to include a small simulation [#] to justify our procedure for kind of experiments that we had conducted with the hardware.

In fact, the new simulation study was included to the paper as a separate sub-section under "Results and Discussion" section. We submitted the revised article, and all the reviewers were pretty convinced with the new results and discussion section.

So, if you want to add something new, make sure that it really is closely related to your work. It should not diversify your present story that is conveyed by your manuscript.

[#] This simulation has to be related to the work you are doing. For example, if you are doing something on security protocols in network, then you could add a simulation showing the energy efficiency.

Your issue seems to be a social rather than a scientific one...

You commented this

Anyway, I don't want to mention the mind-conflict that I have to my co-authors

Why not? What else do you have your co-authors and advisors for if you cannot use their experience?

In another comment you mention something about an advisor not really being an advisor.

Furthermore, the fact that the conflicting input came from your parent should not be of any relevance. In an academic discussion your parent is a fellow scientist and their opinion should be weighed as such.

So, my unsollicited advice would be to get your act together. Do you feel a loyalty conflict between your parent and your advisor? Get over it. Is your advisor not helping you? Deal with the issue.

You need to feel comfortable asking for help/input/advice to those who want to help you. And you need to feel comfortable with not implementing the suggestions you get if you have solid reasons.