Thanks for asking this question. I had the exact same question as you.
Well, not the exact same. I already have a 10-year visa because I've been to China before.
It's my infant son I'm applying for.
I believe that my son is eligible for both Q2 (family) AND L (tourist) type visas. And the purpose of our upcoming travel to China is both for visiting family AND tourism.
Here's some of what I learned from the fine print on the Chinese Consulate in San Francisco website (should be the same rules for all Chinese consulates):
For Q2 visa, you will need an invitation letter from a Chinese relative, for example your father-in-law or brother-in-law. The letter will need to include this relative's name, gender, date of birth, Chinese ID number, current address, phone number, and email address. The letter will also need to state your name, gender, date of birth, nationality, passport number, relationship to the inviter, when you plan to go to China, and for how many days you plan to stay.
For the L visa, you have two options. Option 1 is to submit round-trip flight tickets and hotel reservations for your full itinerary. For this option, you don't need an invitation letter. Option 2 is to have an invitation letter from a Chinese travel agency or individual. For this option, yo don't need to submit round-trip flight tickets or hotel reservations. The letter from the inviter must include the inviter's name, address, phone number, signature, date, and an official seal. If the inviter is a "huaqiao" or "oversees Chinese" (such as your wife) then they must include their overseas residence permit (i.e. your wife's "Canadian green card"). If the inviter is your wife's relative who lives in China, then they need to include their Chinese ID number. For letter will also need to state your name, gender, date of birth, passport number, reason for coming to China, date of arrival and departure, places of visit, relationship to the inviter, and who will pay for travel expenses.