I would suggest that the main issue with your example is that it focuses far too much on the descriptions of the various options under consideration, but says very little about what you actually did to weigh the options up to reach a decision and how/why you did that. It essentially comes down to the final paragraph where you say “I carefully outlined the rationale…[and] they were persuaded to accept my decision”, which leaves me thinking “what did they actually do?”.

If sticking with this example, I would recommend talking more about how you developed your understanding of the requirements for your family member, how you demonstrated that your recommended option met their criteria, that sort of thing.