My grocery bike is an old rigid mountain bike with Northroad handlebars and thumbshifters, Brooks saddle, street tires, and a Xtracycle conversion. I see similar bikes with baby seats hauling one or two kids around, all the time.

I think this, or something similar, would be good for your needs, because:
1. The base mountain bike is rugged and cheap ($100 on Craigslist, then say $100 for new bars, tires, etc), with a wide gear range including the standard MTB 24 x 32 super low gear that will get you up hills with baby, diaper bag, groceries, etc.
2. Northroad bars (or any swept-back bar) give an upright position, with wide tires and a long wheelbase it is very comfortable ride.
3. Baby rides close behind you, can hold onto an auxiliary handlebar when s/he's older, and you don't have the hassles of maneuvering a trailer.
4. The Xtracycle kit is about $200, plus about $100-150 for the pannier rail and pannier bags.

I've seen Xtracycled older mountain bikes for $400 to $700 on CL.

I don't have any problem dismounting by swinging my leg over the top tube, or balancing the bike with 4-5 bags of groceries. But if the load is a baby, then I would add a two-legged kickstand for maximum stability during loading and unloading.

OTOH, a trailer can be buttoned up against rain/cold, while I've not seen a canopy for the bike-mounted baby seats (maybe someone makes one, or a baby stroller canopy could surely be adapted).

I found this article that seems useful:

http://greatergreaterwashington.org/...hese-products/