It sounds like what you are looking for is some degree of mentorship on reviewing.
Many journals and conferences already explicitly support a somewhat different form of reviewing mentorship through "sub-reviewers" or "delegate reviewers." In this system, the person assigned the review can share the paper with somebody else (e.g., a professor to their graduate student) who produces the draft review. The assigned reviewer then goes over the draft review with them, adjusting as necessary, and uploads it with both names on it as reviewer and sub-reviewer (many professors also abuse this as a way to farm out their service work with inadequate supervision, but that's a discussion for another time).
The key point I am making is that, from an ethical perspective, a large number scientific of publications have already set a precedent in declaring that it can be appropriate to privately share a manuscript and its review for the purposes of mentorship in reviewing. Your situation has a different workflow, since you are the one being assigned the review, but the information sharing relationship is the same. Thus, I believe that sharing the review and even the original manuscript would be entirely reasonable and ethical as long as you take the same precautions as one would in deciding on sub-reviewer (e.g., avoiding people with conflicts of interest, making sure the other person understands the confidentiality requirements).
I commend you for the concern you are showing for the quality of your professional service, and recommend you follow through.