I'm in Denmark - feel free to ask any questions or pm me and I'll do my best to answer!
Having also tried being a mum in London for a year, I'd say I definitely find Copenhagen easier (easier to get around with small children, generally quite child-friendly although of course you get mean arses in every country).
Most children here are in daycare - the only mums i know of who have been SAHMs have been expat mums, but even a lot of those still put their children into daycare (most common is from 1 year). Probably the biggest reason I wanted to move back after London was because I wanted to work and financially it would have made no sense if we had stayed in London (we have 2 dcs). So if you are thinking of working, you wouldn't really need to worry about that side of it.
It's a pretty relaxed city I feel - people often turn up to work in jeans etc (except maybe if you're a lawyer or something), most people bike to get around, although there are busses and trains and a metro system. Plus it's not a massive city, so pretty easy to get around.
Supermarkets aren't like the UK - they are pretty limited here and much smaller. There is a much smaller selection of ready meals which is crap when you are feeling lazy
Everyone speaks English - some more fluently than others - so at the very least, basic communication shouldn't be a problem.
Hope that helps as a starting point!