You are right. The possessive form [ name + apostrophe + 's] refers to the home of that person. It's the equivalent of the Italian 'da'.
Note that if you have two names, only the second one takes the apostrophe+s. For example. " I spent the night at John and Diana's. "
With your example, the first one looks fine. I think it's fine to say 'my Aunt Lidia's' or even 'at my aunt and uncle's'. The second one is just about possible, but when you have really long sets of names such as 'my Aunt Lidia and my uncle Roberto' (seven words!), we often add 'house' or 'home' at the end. Seven words is a little bit too long a noun phrase to support one tiny little apostrophe and an s.