Yes! I guarantee they'll have a total blast at a furry convention. Many conventions are open to all ages, and the only stipulation is that you would have to be nearby attending with them at all times. Any such convention takes steps to keep kids from any adult material, such as convention security keeping kids from entering comedy shows or concerts with a "mature" or "after dark" theme, and artists in the artists & dealers areas are required to keep any mature/adult artwork materials in an "18+ only" binder that's kept closed unless an adult is currently viewing it.
One of the best photos my friend and I got from our very first convention was a little girl, I'd guess about 7 years old or so, totally enchanted as she's surrounded by a circle of fursuiters which to her eyes were giant living stuffed animals. I've seen kids at cons whose ages ranged from babies in a stroller to toddlers, to pre-teen and teen ages. I've seen kids at cons whose parents were furries themselves, and those who weren't furries but they were bringing their kid to a con who was a furry (and almost invariably the parents love it so much they become furries themselves).
As far as what you and your kids would see in the open areas of convention space, while the convention security and staff aren't there to babysit every individual's behavior at every moment, there are rules in place for proper behavior and public displays of affection. If someone violates those rules it can result in removal from that convention up through full banning for life, depending on the circumstances. In the 26 or so conventions I've attended over the years (I've lost count), including at the conventions that are only open to 18+ attendance, I have never once seen anything beyond a couple sharing a kiss. Now and then someone wears an outfit that's questionable, but certainly nothing that would be illegal in public. (Note: at the 18+ conventions, the rules of conduct are exactly the same as they are at any all-ages convention. All that changes is that stage performers don't have to watch their language. They mainly have a policy of 18+ only because they don't want to deal with the liability of minors showing up without parental permission, having to deal with refunds of registration in those situations, making arrangements to get the kid back home, etc.)
Long answer short, yes, you should bring your kids to a furry convention, and no, 12 years old is not too young. The two biggest ones, Anthrocon and Midwest FurFest, will be hard to attend because the hotels sold out a long time ago, but the smaller cons should be easily doable.
My bigger concern would be you getting them fursuits. At their ages they will rather quickly outgrow any fursuit you buy them unless it's custom made for a growing kid. Get in touch with one or more fursuit builders and ask for advice on what to do in this situation. You may want to go with a partial fursuit (ears, tail, paws, feet) and save the more expensive parts for when they're older. Or if you all are set on the decision of getting full fursuits, get custom suits that have extra material that can be let out, and removable padding inside the heads so they can be adjusted for your kids' growing heads. Plus, there's the possibility they aren't interested enough in the furry fandom to remain active in it and justify getting fursuits. Definitely talk with them about it to get an understanding of how much they like it.
On a side note, don't worry too much about them getting interested in erotic furry art (yiff). At their age and especially as they get into puberty, they WILL have curiosities and interests in sexual matters whether you like it or not, and they WILL find erotic materials on the internet (whether furry or not). You can't watch them 24 hours a day and you can't shield them from such materials forever; it's unrealistic. What you can do is educate them in sexual matters so they make good sound decisions in life, always view others with value and respect rather than just as a sex object, and with the knowledge that materials like porn are not usually realistic depictions of sex, intimacy, and love.