In a few weeks I'll be going to spend a weekend with my family in a lakehouse. I imagine there will be 7+ people who I'd love to entertain with some great games. Most of the games I own go up to 5 or 6 players, and/or I feel would be a little to complex for them (but I'll certainly break them out anyway!).
7+ is a hard number! I'd recommend a game like Wits & Wagers. It's easy to team up, if necessary, and you can squeeze 8+ out of the game. Another game that works well with a large, non-gamer group is Dixit. You'll need the latest version for the 10+ player board, but you can still do it without this just fine if you are creative.
If your family is really into gaming, then games like The Resistance or Castle of the Devil would work well. These require more emotional investment and/or role playing than most families can handle, but they do handle large player counts.
It's not so much a gamer's game, but Catch Phrase! is great for 6+ players if you have an even number. It get interesting with family members because you can use a lot of inside jokes to your advantage.
Bonanza was really popular with my family. I took it to the family cottage several years ago, and some family members have since turned into casual gamers. Bonanza can play up to 7 but I would say 5 is the best number to play with.
We had a lot of fun with Survive: Escape from Atlantis!. Nothing like taking out your sibling with a sea serpent. You can get an expansion to get you to six players, but I'm not sure how well it plays. If your family is like mine, not everyone will want to play a game at the same time, so you may be able to use some that handle 4 and 5 players.
Wits & Wagers was the first game, and came with about 700 questions.
Wits & Wagers Family was the second game, and game with less questions, I believe, but all the questions were targeted to a more general audience.
Wits & Wagers Party edition has approximately 200 questions, mostly from the Family Edition. They took their favorite/most fun questions from the Family Edition and used them in the Party Edition.
There was also an expansion for the original game that had an additional 700 questions.
Personally, I like the original game best, because there are more questions in it. It's easy to take a card and pick the most "family friendly" question on it. My family likes the betting aspect, but I can see how a group of 10 would be better of with just a few points on a score track. But there's no reason you can't score that way anyway. Betting is optional.
Either way, it's a great choice for the family. The most fun aspect to me is how people talk about the questions before revealing the answer. You get a lot of fun tabletalk about how grandma knows the answer because she was there when the combustion engine was first introduced, and her answer has to be correct. And then you can get ridiculed when you refuse to bet on grandma, and she turns out to be right. It's a great party game!
Disclaimer: I designed it. Disclaimer on the disclaimer: I designed it just for the purpose you describe. All my favorite games play at most 6 and we always have at least 7 so I needed something that a group could enjoy and still satisfy my gamer soul.
Be aware that some people really hate trivia games, and those people hate Wits and Wagers rather more than they hate other trivia games.
I have not found this to be the case with Wits & Wagers at all. I have seen people who hate trivia games play this game and love it. There is no pressure to know the correct answer, you aren't expected to know the correct answer, and most of the questions are such that people know the approximate answer anyway.
I won't tell you you are wrong, because I'm guessing you had a different experience than I did, but I want the OP to know that my experience differed completely.