I was offered a job on Sunday the 29th and accepted on Monday the 30th with an expected start date of the 7th. I was just given another offer at a company where I had also interviewed for more money, more room for growth, and significantly less travel. Right now, the second one is a much more attractive offer. It feels like it would be rude to quit before I even started the first job, but the second really is a much better fit for my family. Would it be okay to
quit suddenly like this? What should I tell them?
It is your privilege to take the better offer! It's actually great that you haven't started yet. It is one thing to say "On second thought, I'm going to decline" and another thing to quit the job on the third day or second week of work. There is no ethical or etiquette problem involved in quitting a job you haven't even begun yet.
I'd call your hiring manager and say "You know what, I'm not going to be able to start the job as planned on the seventh. I wish you and your team all the best." That's all you have to say. You don't need to tell them you got another offer, or tell them where you're working. As far as they're concerned you could have won the lottery or decided to join the circus. The less said the better, and you don't need to apologize, either. In this era when each of us is driving the bus of his or her own career, the simple message, "Thanks anyway, but I'm going in a different direction" is sufficient.
If the offer had been more competitive, you very well may have passed on the second offer. Employers who don't keep up with the market unfortunately get used to having people bail early on in their employment -- or even, as in your case, before they've shown up for their first day at work. Think of it this way: you're providing valuable information to that employer. It may be that the next person they hire will come on board with a more competitive package that will make him or her less likely to bolt before the ink is dry on the offer letter.