I think @DeedlessIndeed advice is good - but you are also right to limit the stress on your own children. If your DN is very traumatised, it may not work out and end up with him going into care anyway.
If I was in your position, I would approach it in a two stage way - rather than it feeling like an ultimatum for your partner, you both need to frame it as what is best for the children - all of them.
Firstly I would make sure that Children's Services do take him into care, but your partner should agree to take DN in as a Kinship Carer - do not accept the solution to be a privately arranged Special Guardianship Order which is what they may push for.
By DN being formally placed in care - even with your partner, you get access to a multitude of support that would not be available under a private SGO including foster care payments and support, breaks, possibly things like reduced council tax, free access to leisure services etc depending on the foster carer offer in your LA. You may even be able to get some support around the renovation - children's services can help unblock any issues with planning and there may also be access to grants to help with the extension if cost is a factor in the speed at which it can be done.
Your DNs school would also get pupil premium for him if they don't already which may help fund additional support for him through school. You can also push more easily for trauma counselling (depending on local policies and availability).
By being taken formally into care rather than a private SGO, it also gives you all a period to see if things settle down. If they don't, it will be much easier to ask children's services to find another placement than it would if it is private SGO.
In terms of the two of you, I would frame the situation as a temporary one - you live separately to give DN a chance to settle - it will be traumatic for him, on top of his existing trauma and his behaviour will be up and down for a while. It will be much better for him to have some undivided positive attention for a while.
You can always spend weekends together which will give you all a chance to see how things are starting to settle.
As your DN settles down, you can start to increase the amount of time you all spend living together until you get to the point where hopefully it can all become permanent.
Doing it this way will allow you all to see whether things are going to work out and if your partner can't meet DNs needs, it will be less traumatic for him to go into another care placement if he has only been living with you partner than it would if he was moved from living with the whole family which would make him feel much more rejected. It would also be less traumatic for your children.
If it does work out, it can be a slow introduction both for DN and your children, where expectations can be addressed on all sides and give you chance to sort the rennovations out
He will likely need support for years - but at 10, there is a very good chance that on a day to day basis, with a lot of love and security, that the worst behaviours can be addressed relatively quickly.
It may take some doing, but there is a middle ground which means that you both have the chance to change the life of a little boy for the best, without it having to negatively affect your children - it will just take some compromise and sacrifices on both sides for a little while.