Is the following sentence correct?
We gathered in our grandparent's house
can "in" be replaced with "at"?
What if "house" is replaced with "home", does that make any difference?
Abishek is correct about at being used to refer to a specific place such as a house rather than a town or a country.
But at and in, as prepositions to a specific place-name, mean slightly different things, certainly in BrEng.
We met in my grandparents' house means that when you met, you were [both] inside the house.
We met at my grandparents' house means that you met in the general vicinity of their house, for example in the garden or at the front gate, but not necessarily inside.
The use of Home vs House makes no difference here.
Preposition for place like home, school, office or any general places can be filled by at and for places like countries and cities can be filled by in at times.
In, as a preposition of place, is usually used to talk about the position of someone or something inside large places such as countries, continents, big cities etc.
For example:- She grew up in New Zealand.
At, as a preposition of place, is usually used to talk about the position of someone or something inside small and unimportant places such as villages, small towns etc.
For example:- I'lll meet you at the pub.
Yes, you can use "at", but the meaning changes slightly. Gathering "at" a house allows for the possibility that you all met at the gate, but didn't go inside. Gathering "in" a house leaves no doubt that you entered.
(In my experience, British English speakers make this distinction more than American English speakers do)
The word "home" carries an emotional attachment, whereas a "house" is simply a structure. "Home" can be a larger thing too: "we gathered in our grandparent's home" could mean that you met in the town where she grew up, or it could mean that you met in the small apartment that she used to live in before she moved away last year.
However, if you say "house", then you're definitely gathering inside the building where she lives (or, of course, a building that she possesses).
(It used to be that only real-estate agents said "home" when they really meant "house", but I've noticed it creeping into American usage in the last few years.)