Can someone mind your DD for the day? That will free you up to deal with the move without having to tend to her, plus she doesn't have the disruption of the move unsettling her.
If possible it might be worth using the same removal firm to co-ordinate things. If you have the budget, I would pay for the removal firm to do the packing - they'll come in the day before the move to do the bulk of it.
If you have the removal firm do the packing, have an area set aside for things you are keeping with you and taking in the car so you don't end up with essentials packed away and you can't find them. Things like: bedding, kettle, tea, coffee, milk, documents, a change of clothes, towels and cleaning materials.
Make sure both houses are packed up by 12 noon, exchange keys, drive to the new places and unpack.
Ime, people doing their own moves vastly underestimate how long it is going to take them and are far less experienced at dismantling furniture to go in the van then putting it back together in the new place, which is one of the reasons it takes them longer. They also tend to make boxes too heavy, which makes moving them much more awkward.
Declutter as much as possible now. Hire a skip if necessary - it means you don't have to make multiple trips to the tip, etc.