I did a move at 38 weeks with a 1 yr old
I packed rooms into
essential for first night (kept them with me in my car)
Needed pretty sharpish (packed into boxes by room)
Nice to have (packed into boxes by room)
The needed pretty sharpish I put florescent green duck tape on the corner
The nice to have i put blue duck tape on the corner
The fragiles i put florescent pink duct tape on the corner as well as blue
All the green boxes went straight to the correct rooms
All the blue and blue pink boxes went to the garage/attic
That way i had the house pretty toddler proof in 2 days and was able to just pull one box out at a time to unpack slowly in the following weeks
The trick is to think really carefully what you need in each category
Put a piece of painters tape on each piece of furniture with the room it is going into. Tell the movers to peel it off and put it onto of the wrap of anything they wrap
Also do you need to put a stair gate up before the toddler comes home
Do you need curtains or blind in the toddlers room (a towel stuck up with masking tape will work for the first night)
Pack a tool kit with screw drivers, batteries, tape, box cutter, tape measure, work gloves, toilet plunger, bin bags, paper towel and paracetomol. Kepmit in your car
Get a folding chair and plonk it by the front door as they are unloading the moving van. Sit there and tell them where each box/piece of furniture goes as it comes off the van
Organize some friends to come and unpack the kitchen. Stick a label on each drawer and cupboard of what you want putting in it. Dont supervise
You unpack the toddler and new babies room so you know where everything is (and you are nested)