I kinda know where you're coming from. Got two kids myself (age 8 & 6) and I ride through East & Central London every day, and yes, it's a stressful ride at times. Admittedly I only started riding when the kids were toddlers and sleeping through the night, so not as bad as having a babbie. I'm going to echo most of the tips already said, but in my experience I found these help:
Don't ride after a sleepless night or when run down, you just make stupid mistakes and don't spot obvious things idiots are about to do. Take alternative transport or work from home if you can.
High viz certainly isn't going to make things worse. Although there are arguments for wearing as much solid colour as possible, rather than breaking silhouette into many coloured areas. I currently have a Fluro helmet which I think helps.
A loud air horn like the Nautilus really is useful. I use this a lot and really makes a difference! Loud cans also really work too.
When I first began riding, I was always opting for too high a gear. Especially in heavy traffic ride in lower gears, keep revs in mid range: 4-8k odd. Then you make more noise so more noticeable and you've got more acceleration and engine braking on hand if you need it.
Gear up. Wear as much blinking armour and protection as you can. Get decent waterproofs, layers, heated gear for the shit weather days. If you're cold or wet, your concentration lapses, which you can't afford to let happen.
Consider a helmet cam. So when you do have an incident, there's no messing about with liability, made up witness and other such shite that just causes on going stress for months, years afterwards.
I've no idea how much riding experience you have, but consider a BikeSafe or IAM course to bone up further on riding defensively and safely. It may not be super exciting, but it all helps and makes you think more about how you can possibly ride better.
Don't give up on the bike entirely, when you're little 'uns get a bit older then bike really helps get you around quick enough to work around childcare arrangements. It's only with my works flexi working hours and the bike that I can get to/from childcare in time to make it doable to have both of us working. Just wouldn't be possible via tube/car.