There are two potentially correct options available to you. In order to deem which one is most correct, one needs to look at the context in which this script was written. If you are meant to be talking to the nanny herself, then the correct answer is : If we had a nanny like you, we would treat you like gold. If you have written the script so that you are merely talking about nannies in general and then using a particular nanny as an example of what an ideal nanny should be, [in other words, you are having a conversation with somebody else and chose to illustrate a point by bringing up the example of a nanny you both already know, in order to illustrate how you would treat a suitable nanny, if ever you find one] then the correct answer would be: If we had a nanny like her, we would treat her like gold. In neither case, however, would it be okay to use the word "got". one would have to use the word "had"... I hope that helps!

if we HAD a nanny like you at my house, we would treat her like gold. Which one is more natural?= it is not the question of being natural, got is simply wrong. Do they mean different respectively?= no, when you use got, it becomes meaningless. or Are they interchangeable?= of course, you cant change a correct word with an incorrect one. on a side note,there is nothing called HAVE GOT, only HAVE suffices.

ANSWER If we HAD a nanny like you at my house, we would treat YOU like gold. 'If we got' is incorrect.