I worked for 9 years in one of the largest city firms. Mixture of transactional and regulatory stuff - mostly transactional in the boomtime. Had my dd when I was 4 years PQE and came back to work full time. However announced that on Fridays I was working at home, and this seemed to be accepted. Fridays I took calls from clients, worked when I needed to, had the day off when I didn't. I felt that instead of being paid for 4 days and working more, I would rather be paid for 5 days and work less if at all possible. By doing it that way I also didn't get labelled as a "part-timer". Then had ds at 6PQE and went back again on the same basis, but found it much less satisfactory. Actually there were quite a few banking and corporate partners who were trying to do various methods of flexitime - some took additional time off at the end of transactions, one took 9 weeks a year holiday instead of 6 to be around more in holidays, some tried to do 4 day weeks, none were really particularly successful or happy with it. Maybe it is easier now that the workload has generally gone down (although the pressure to perform has gone up).
A few of my peers went into PSL work, but that would have driven me mad (and bored most of them) and wouldn't have matched my ambitions.
Anyway, in the end I was within 2 months of my partnership decision, dreading going into work every day because I had just had enough, and a client made me a really interesting offer to join in an executive, non-legal role with a chunk of equity. I said "can't possibly" he said "why", I said "I'm going to make partner and THEN look for something I really want to do" and then realised how idiotic that was. So much to everyone's surprise, I set off on my new adventure. Now work 4 days a week, 2 of those days from home, haven't looked back and much to my surprise haven't missed the city or the firm for a second!
This is very long and probably not very helpful - but my main advice is to really think about what will work for you, then go to your partner and say "this is what I would like to do, this is why I think it would work, I would like you to let me try it for 4 months and then review it with you to see that both of us are happy". Make it very unreasonable for them not to do it on a trial basis.
In my opinion they don't want to hear about job shares, again, if you want to do this, set it all up yourself, find someone who wants to do it, work out exactly how it will work, and then present it to them as something you would like to do for a trial period. Once you are doing your trial, they will realise that the world hasn't ended or alternatively they will try and get you to go back to how you were and if so, you will be in a much better position to judge whether you are willing to do so or not.
Best of luck! It is a killer, as I always say maintaining a career and a family is always one huge compromise.
Sorry this was so long