My gut feeling - miso - is stick at it; try not to make any unnecessary sacrifices.
I think work from home/find another job suggestions may be a bit of a red herring - you might end up investing lots of time into trying to get something off the ground, just to find yourself working longer hours for less money in something that you enjoy less. Trading is pretty unique (for better for worse) as a working environment.
Having said that, I'd definitely try to have the balls to manipulate my work situation.
You need to start off with an ideal scenario and see which bits of it might be achievable. What upsets you most about current situation? Unpredicatability? Bringing work home? Not having one free weekday with your girls? Total number of hours spent with your girls?
Then be ballsy about trying to get it. I always think that if you're too timid to fight your case on what is important to you personally, then you're probably too timid to fight your companies corner professionally. That is, consider it in the same light as any other political negotiation you do at work.
If you've been in the industry for a while, you probably have decent contacts... anyone out there who may be interested in poaching you in return for better terms... any working mothers you know whose experience you can benefit from ... presuming you've asked your boss? A slight sideways shuffle (e.g. becoming a structurer, or an analyst)might make this more achievable.Have you considered working contracts? A different city (a bit of a long shot, but perhaps doing a stint in Europe will get you 'off the radar' enough to allow you to work shorter hours, without leaving a CV gap).
A friend of my Dh works on a trading desk (but admittedly not a trader - more of an IT dude). He has a great thing going where he and his family live in scandinavia; he travels to london one week in every four and teleworks the rest of the time. He cycles his kids into school every morning; and seems to pull a lot of late nights to get the work done.
I think you should be proud to have done well with your career - and I think your Dds will be proud of you too, so long as you set things up in the way of 'grown ups have to balance a lot of demands on their time' rather than 'the office always comes first'.
Don't feel guilty about working per se. Go with your gut instincts on what the real issues are for your family. and to try to figure out effective solutions, rather than just be blown about by other people's world views.
How old are you? Only thing about trading, is that I don't think it is realistic for people to speak of a thirty year career ahead of you in the same field. Traders' careers are about as long lasting as premiership footballers. Depeding how near to forty you are, you may in any case need to start developing a 'Plan B'.
I'd be ruthless on cutting all the other crap out. Make sure that you sacrifice all the less important stuff before you cut on things that matter to you. Move to Discovery Dock (or wherever is immediately next door to your work); cut out the commute entirely. Have the full suite of cleaners/concierges/assistants to deal with chores. Don't sweat dull social engagements. Accept that you don't cook; buy your clothes in capsule once a season; take hair/make up time down to as near zero as you can.
Good luck with it all. Remember - what matters it what works for your unique family. Your girls won't love you any less or develop any worse just because you work. But you do need to be true to yourself, rather than be bullied into maintaining the status quo.