Feijoa, have a good look at a marine chart before you go so you can see where the hazards are, namely sandbanks. Navionics has a webapp to view the charts and zoom in to points of interest.
In particular Mair Bank on the right as you exit the harbour.
Safer to exit in between the red and green marker buoys, ie remaning in the channel. And also note the other banks in the harbour.
As to fishing about now is the time of the year the snapper move out of the harbour so can be hit and miss although maybe safer for your kids.
The entrance past the Frenchman can be ok as is further down the channel, but with the enormity of Bream Bay take your pic given the sea condition. The chicks is always hot or cold, one of those you never can tell its worth the journey.
Along Peach Cove towards Bream head I haven't had much success but some do get lucky, I suggest to drift along to prospect the area, work out to the end of the weed line about 30+m or find structure holding fish and then anchor and apply berley... plus it is a busy traffic area being on the edge of the main channel and in my opinion is thrashed...divers and fishers.
47-50m off the "ole Woman is the winter tarakihi spot, they will leave us soon, find last 2hrs towards high best, sometimes at mid tide the current is too great and fish move off or rather the boat moves off the correct angle, you need to anchor here, although some still drift and do ok.
End of Fairway bouy during an incoming can be a good indicator of if the fish are coming into the harbour, but we find not until Nov and then in the harbour itself, jan feb and march are best months.
But inner harbour fishes diffrent to outer harbour so two different ball parks.
The end of Bream rock or the "Ole woman has some good under water reefs off it worth prospecting and from there northwards between the beach and Guano is lots of rocky foul, drift and softee it...
Bream Island or Guano rock can be good with schooling fish (kahawai, trevs, macks) and big arse kingis have been regulalry taken as do Back marlin in the summer.
From here northwards you can explore ocean beach and head towards Kauri Mountan coast which is great rocky reefy area all the way up to Taiharuru with the odd bays and rocky headlands all the way up. At the end of Oceans is Awarua Rk many big snapper have been taken here, 3 big reefs out the front that awash on the tides to watch for...but the area can be amazing, years ago my mad mates used to swim out from the beach (400m) at NIGHT and fish it and yes regular 26 up to 29lbers!
Head east of here and some good lumps and bumps from 30m out to 60-70m and so these continue all the way back to the Chicks Islands. Good for Tarakihi, reef fish, snaps and small puka, blue cod, sharks, etc.
Coming back to exiting the harbour there is Busby Point which if you anchor about 200m towards Peach Cove can have great kingis come past at the right time of the year (50lb) (used to be 100lbers in the old days)

if you are patient to deploy livies or strayline pipers, otherwise during the season have a cast and throw poppers around the harbour channel marker bouys, even stickbaits or tow rapalas too.
Carry on out of the harbour following the bouys all the way out to the end - Fairway Bouy sort of head to the Hen Island on the right of the chicks and about a mile away you should be approach 3 Mile Reef, this covers a wide area and is basically low level foul, it is home to many reef species and other fish like snaps and pilchards school up and around it, it is a hit and miss place, sometimes it is a place to save the day with a John Dory and Fat Blue Cod to have for dinner where all the best spots failed...but myself have never done great there...
Between that and the Fairway bouy in about 22m of water can be a good place to start drifting if the wind is ok and you have a sea anchor, use a bait straylined off a ball sinker or two and drag reasonable sized baits over the bottom, even flasher rigs with baits work, put these gears in your rodholders and drag them with a medium drag to set the hook when you get a hit, and then deploy your softbaits, so using two techniques to maximise the attraction and capture methods on the day.
So drift around 22-26m before 3mile reef as above, also try in at 16m and work out to 22m, by all means if you go over good bites then mark it on your gps and go back and repeat your drags over the area. This area you will get gurnard and snapper. (my mate took a 15lb Hapuka here over the sand!)
Look at the shore at Ruakaka to the right where the power station building used to be directly in front is 4 large yellow bouys, sometimes you will pick up kahawai here and the odd small just legal kings, trevally and other baitfish...
Out off the Power Station in about 10m is a hole sometimes Gurnards and sometimes good Snapper, in fact drifts any where along here off the beach can be very rewarding fish up to 16lb.
Then carry on south looking at beach Ruakaka again and find the Racecourse building - white and low rectangle, again 10-16-22-26...
And then repeat the same process and depths heading furthersouth off Ruakaka river mouth, Uretiti, Golf Course, Waipu River...and all the way down to
Off the Waipu river mouth is a small reef in 16m that is worth dragging everything over and also deploy your rapalas and have a bit of a troll as there can be great kingies along here.
Further out off the river is another bit of foul and reef in I think 28m, another place to have a drift passed and see if what is awake.
About end of Oct early Nov should see big workups of pillies schools with snapper, kingis, makos and other predators feeding with gannets galore, go out to about the 35m mark and drive southwards and then easterly areas out at 40-45m (towards Hen Is) and you should find those spring snapper workups, hit them again with either softees, dragging baits or even metal with jigs and inchikus...