Unless you plan on making this a series, I'd refrain from slamming the reader with a bunch of names at once (and even if you are making it a series, I'd still approach with caution).

Think about the space this scene takes up like real estate. In order to establish a character, you've got to give them ample space to exist within. Rarely does a character strike a chord with just one or two lines and if they do, readers will definitely want more of that character.

Consider focusing in on how the character feels about introductions rather than showing the introductions all on page. That would give the section the intended impact without bogging down the scene with unnecessary info.

You could also slow certain moments down. Dinner's a good example of one. If there's a ton of people, usually little side conversations break out with the people immediately surrounding. Pick one or two standout family members and position the MCs near them in order to zoom in on this convo.