Two things about your family. The first is- it doesn't really matter how they take it. Even if they take it poorly, it's more of a situation that is then on you, whether you can proceed despite their objections. If you can't, that's what you need to work on. Trying to change them is a much less efficient route to take. With that said though, the best explanation you can give them is the same explanation you are giving yourself as to why you should proceed with REI. If you aren't clear enough on exactly why you're doing it to be able to explain it to them, you aren't clear enough on it within yourself and you may want to clarify that. We all know generic reasons why it's good to invest in REI, but what are the deeper reasons and more thought-out reasons? Part of that answer is likely going to be in understanding the numbers, how you plan to profit with a certain property type or strategy, etc. When you can give uncontestable information as your explanation on why you feel good about moving forward, you're a) more likely to succeed yourself and b) going to be less dependent on other people's opinions.
As far as buying a primary and turning it into a rental in a few years, just make sure you understand all the numbers so that when you do turn it into a rental, it can actually be profitable. Especially if you do loans under 20% down and end up with PMI, that's an even bigger hit. So make sure you know what you're doing there, but you definitely have time to figure that one out.