For noise I recommend a noise cancelling headphone, BOSE QC35 is good at it, sometimes I'm wearing it on without music and it's enough.

We have two kids, 7m and 3y-ish, while the older is at kindergarten I do sync work with others or do focus work for about 4 hours.

When the older is back home I only do one meeting (rare) or push something that really really really needs to be pushed. After they go to bed I catch up on deep work for 2-3 hours.