In my opinion a small dog can easily co-exist with a large dog, but it depends on the individuals. I know a lady who has 5 or 6 large dogs and one really small mini schnauzer (less than 20 pounds). Your labs would probably just have to be gentle when playing with the dachshund. I've seen some dogs automatically become gentler when playing with smaller dogs, but if not you'd have to teach them. The other thing to keep in mind is dogs are relatively sturdy. I don't think a rolling lab is going to snap the dachshund in two.
As for children, I think it really depends on the individual. If you get a puppy and make sure he has lots of positive experiences with children it should be okay.
You will want to make sure you socialize it early. They can be mean to strangers otherwise.
That's my two cents. I'm not an expert on dachshunds, though.