I have a 1/2 acre lot in the suburbs. I have 5 children, 2 of which have been through the 9 mo phase (youngest is now 18 mo). I've also got a small orchard and a garden here. I can keep the bees in a back corner and there are good trees all along the lot lines.
We mostly get wasp stings around here(7 year old boys aren't very smart!!) . The honeybees only sting when I'm messing with them or if the boys (7&8yrs old) are messing with them. One time my 13 month old son (now 3) did crawl out there and try to stick his fingers in the hive...the bees swarmed around alot, but only caused 2 stings, one to the 13month old, one on the 6 year old that helped out and grabbed him away. That is when the fence went up, although not all of the hives fit in there anymore, but there haven't been any other incidences, I don't tolerate mean bees.
They will take more time than you think. Once you have them for a while it is about 1-2 hours per week. Initially though you will probably obsess about them and spend as many waking hours as possible watching or monkeying with them or the equipment. My wife complained all time about how much time they are taking. This year has been a little bit better now that the little kids are a bit bigger and I'm learning to leave the bees alone as much as possible.
good luck convincing her. My wife looks forward to selling the honey for me. Great for gifts too.
PS I will also add that my 8yr old son really is getting involved, and now has his own hive, it is really neat to see him get excited about all that. That is enough to make his 7 yr old brother jealous, so we will see if he gets more involved.