Questions like that are what you'd ask if are in a relationship. Asking who with is now a no no, asking how long is fine as you would need to know how long you have child for.
Please take on board the advice from the others re controlling behaviour etc.
At best she could just be making it clear to you where the boundaries are and you just need to focus on your self and co parenting. At worse she could be setting you up by pushing these buttons and gathering evidence of your controlling, coercive behaviour with a view to claiming DV.
If she goes down the DV route and if you have given her plenty of examples then you will inevitably have to leave the family home, often without any notice if she gets a court order and contact with child will stop too, forcing you to pursue court process to see child.
Feel free to research conrolling and coercive behaviour online so you get a better understanding of how it can be used in the family courts.
If you haven't already it might be worthwhile sorting out who has child on what days/weeks so that you can get on with your own lives and avoid situations like this,
When you say defending the divorce, do you mean contesting it? If so, in doing so, it can delay the divorce from 2 years to 5 years, but in reality, what would it achieve? It wouldn't save the marriage if she wants to divorce, and it would make the proceedings far more acrimonious and delay both of you with moving on with your life. I wouldn't recommend following this course - you are better trying to come to some amicable way forward if that's possible.
Ok, I have agreed to the divorce. She’s started mediation but I don’t expect to agree on the house, neither of us want to leave. What is the likely outcome in court? I’m hearing that it’s likely I’ll be asked to leave the house and I’ll have to carry on paying half the mortgage. That doesn’t sound fair, she’s the one who wants to end this!
You need to accept that this is going to happen, and the reasons, or who wanted it are irrelevant as far as the court is concerned. Your original post said that she wanted to buy you out of the house, and in my opinion, that is a good outcome, and potentially better than a court might impose. My personal opinion is that you should negotiate to get a reasonable settlement for her buying your out - she paid the deposit and earned more than you so so she has an argument for a greater share of the equity, if you agree to a settlement, you may get a slightly more generous settlement to avoid further legal expenses etc, but what you must not do is argue for more on the principle that she wanted to end it and you didn't, you will almost certainly lose out if you try that.
Also, do not accept paying (or giving away part of the equity) as a lump sum in lieu of paying child maintenance - the court would allow that, but CMS can override that in 12 months so you'd lose out on that - you need to be paying child maintenance in accordance withe CMS calculations (ideally, open a case with CMS now - costs £20 one off fee) and the court will accept that.
with child arrangement orders, majority of times it's the mothers who are given primary custody of kids. they can assess both of your situations like working life and availability to care for kids. it may be possible to have 50/50 care, but it's hard to achieve from what I hear.
I am not experienced in these matters, but from what I have researched, court generally looks at stability of children. So if they decide that its in children's best interests to remain in the house with the mother, then that's what they may rule.