As other have mentioned, there's many possibilities, and if you buy top quality gear you won't be disappointed.

That said, "top-quality" doesn't have to mean bulky and expensive. The EF 100/2.0 is faster and sharper than the 70-200/2.8 L and four times less expensive. It's also much, much smaller and lighter. I own the 70-200/4, which is already twice as light as the /2.8, and even that stays at home most of the time because I just don't want to bother.

A photo belt with the three /2.8 zooms (16-35, 24-70, 70-200) strapped to it is a frightening sight. It's definitely a good choice for a professional event photographer on assignment, but chances are you won't want to carry all that for a stroll in the park with the kids.

Regarding specific lens suggestions, I wouldn't bother with a mid-range zoom. You have one already, and although it's cheap plastic, it does actually take pictures. You'll probably want to upgrade it someday, but right now I think you'll get more from either a fast telephoto for close-up portraits or a wide-angle for environmental portraits.

Specific lens suggestions :

WA: 16-35 /2.8 : it's big but not enormous, the range is great and it will work on a 5D if you buy one one day.

WA Alternatives : 10-22 EF-S : much cheaper and wider but slow and won't work on a 5D 17-40/4 : no advantage over the 16-35 except it's cheaper 28/1.8 : best cheap solution imho.

Telephoto: 100/2.0 : very small, super fast, not expensive. I love this lens.

Alternatives: 70-200/4 /2.8(IS) : imho too big and heavy to use in "social" situations. They make very good sports lenses though, so you might pick one of these when the baby has grown a little and starts running on the lawn :-) 135/2.0 : I don't own it but most owners swear by it. 85/1.8 : very similar to the 100/2. I like the 100 perspective better but maybe that's just me.