YANBU to feel it is not appropriate for him to discuss this with his girlfriend who has just moved in with him. I think 'partner' is a bit of stretch. in his shoes I would be a bit worried she seems very grabby for someone who is only just moving in and when he is legally married to you still! But appearances can be deceptive, so keep an open mind!
Re "He keeps suggesting that it's causing issues between them"
As others say, not your problem, make it clear it is not your problem and will... butter no parsnips with you!
Re " ...and she is pressuring him to get it sorted out soon"
Just tell him you and he will sort out all details, these affect his daughter, who is only 4.
He should be putting his daughter first and providing a fair assessment of his assets.
Re "... he is discussing the intimate details of our and therefore my financial situation with someone I haven't even met." I am afraid I agree with others you can't really stop him. You could tell him this makes you uncomfortable and I agree it is unreasonable of him (IMHO) but if he is being an arse this may just make him do this more!
He has created this situation by allowing, or even encouraging her, to move into his home (or he into hers, or whatever) before he has finished sorting out the details of your marriage.
Re "he is unfortunately throwing her opinions and feelings into our discussions about it all which is making me angry and tbh I don't care at all how she feels and believe that this is between us to decide." Just tell him, as said up-thread, repeat again each time, 'this is between us'....
Re "I haven't met her yet (that's coming next week) and as quite a private person I feel uncomfortable with it all." Hope the meeting goes well. Just remember although he says this is the case (she is pressuring him), it may not be so! When my elderly relative re-married a much younger women he portrayed her in a certain light (she had to be called Blah Blah not just Blah) etc, the impression was she was very snobby etc. After his death it was discovered that all this was his interpretation and the lady in question was fun loving and nice and happy to be known just as Blah!
PS -
"It hasn't helped that he is being an arse about it and trying to hide his assets and business interests."
Who is your solicitor, get her or him on the case (I've watched too much 'The Good Wife' but I do think solicitors might be able to work miracles!).