Pretty nasty situation and my heart goes out to you.
Can I assume, first of all :
That there are no children ; and
That the house is in your joint names.
On the assumption that this is correct :
Firstly, you may not want to divorce him just yet but unfortunately you have to accept that he may try to divorce you. Everything you say suggests to me he wants to sell the house, a.s.a.p., and marry the OW.
Secondly, bringing the OW into your house is insensitive to the point of callousness, and is to be deplored. Now normally one of the rights a property owner has is the right to exclude from the property people whom he does not want there. So if he does try it on I would at least take legal advice with a view to having the OW excluded.
Unfortunately, as you realise, it takes two to make a marriage work, and if one party is determined that it will not work there is little the other can do to prevent divorce. So we can have to do a bit of crystal gazing and try and anticipate that might happen in that eventuality.
What we have here is :
A short marriage ;
No children ;
Both parties, I assume, comparatively young ;
With equal incomes.
Now all of those factors suggest to me that the likely outcome of a divorce is that there would be a
Clean Break, the house would be sold ( or one buys the other out ) and there would be little or nothing in the way of ongoing maintenance.
The fact that there are uncompleted works to be carried out is undoubtedly a complication, but let''s leave that aside for now. If you get into a divorce situation, then the Court would look at the housing issue and would want to make sure that you both had homes. The fact that you expended money improving the house is not irrelevant, but I think I''d better warn you that the parties'' need for a home would be regarded as more important.
But there is one factor here which I think you can use, that being that, if he intends to marry the OW, then there are two incomes going into his new household, and so, while it is emotionally hurtful for you, the fact remains that his new, household, with two incomes, could afford a larger mortgage - and in your position I would argue that this factor alone justifies a higher share of the proceeds for you, and that a 50% split, which he clearly wants, is not appropriate.
The other issue is that you do not want to spend good money on improving a house which may have to be sold if the result would be, say, that you spend £10,000 and get £5000 back. He may well be thinking on similar lines, but doing the repairs prior to sale ( something I would normally advise ) merely makes the house more saleable and thus brings forward a situation you want to avoid. If you want to buy him out, leaving the works incomplete depresses the value of the house and makes it more affordable for you.
Anyway, there''s a few thoughts and we shall see what, if anything, other posters think.
LMM