I think you are overthinking this.
Are you really going to be doing little jobs around the house in the next 2 weeks ?
as that is about all you have left until you move - Sept 8th ish isn't it ?
Is the van yours or a company one ?
is it secure ?
as you could start now by putting some of these tools and all the other valuable stuff in it, every day for a week.
Is there a secure yard or something at work that you could leave the van ?
can you drive the van to work one day and get home by another method ? i.e. walk ! then use the car thereafter to get to / from work.
if needed you could give some elaborate excuse as to why you don't have the van i.e. it needed a MOT and failed and it's going to take x days to get the required part etc. - think out of the box !
If there is nowhere secure to leave your tools at work, then you could hire storage for a couple of weeks. where I live there are lots of storage units around, fully secure with staff on site and 24 hour cctv.
A very quick Google tells me :
Size of storage 50 sq ft
Cost for 1 week £22
Cost for 1 month £95
Now the car, you could easily start getting your clothing into it, every day another couple of items.
Yet again think out of the box ! does the girlfriend and her mother actually see you leave the home every single morning ? you could wear 2 shirts one day under a jacket, or two jumpers, or a pair of jeans on top of another ! then drive round the corner and take off the 2nd shirt / 2nd pair of jeans whatever. Fold up and put in the boot.
Can you get out the house in the morning with a pair of trainers in a carrier bag ? yet again put it in the boot.
What do you have / need in the way of personal possessions i.e. passport ? gadgets ? games/gaming stuff - you need to think this through. make a mental note of what you actually have and how you are getting it out and where it is going until you can move into the new place.
Obiv she will notice if all your clothes vanish, so choose the newest / favourite / best items to move elsewhere.