Hi OP, so sorry you're going through this.
I'm in the process of divorcing as well. My husband moved out in July. We have both independently seen a solicitor to check the law about financial settlement, as well as researching it ourselves. In our case we are trying to stay amicable and my husband seems to be taking a fair approach so far. It's really hard to keep emotions out of things though!
I recommend you look at the Advice Now website:
www.advicenow.org.uk/guides/sorting-out-your-finances-when-you-get-divorced
It's a UK site and it's absolutely fantastic, goes through divorce and separation finances in great detail. Very easy to read and you can download their help sheets. I highly recommend you read it as it will help.
Mediation should help, but ultimately they can only advise. It might however help your husband understand what is legally acceptable!
As you have dependent children you would definitely be wise to get legal guidance as the rules vary according to many factors.
Basically though the courts will look for a fair settlement for all sides, the welfare of the children will be a major influence.
If you decide to divorce, you will both need to agree a financial settlement/consent order which either you can draft yourselves, or a solicitor can draft it for you. (Cheaper to do it yourself if you can reach agreement then the solicitor will just check and sign it).
Before the divorce is finalised, this document will be routinely checked by the court to make sure it's fair. It can be rejected if not fair to either party.
We were told to try to agree and much as possible between us, because the alternative of getting a court to decide how to split finances is really expensive (can easily cost thousands which will ultimately come out of both your money).
You can get a free or low cost initial meeting with a family law solicitor to discuss anything in more detail (the Advice Now website also has solicitors you can call). My husband had a free half hour meeting. With my own solicitor I had an hour which was £100, and he was very helpful in explaining how the process works.
My solicitor said it's a relief when people work together and that a lot of partners try to argue it shouldn't be an equal division of assets.
Be careful not to agree anything without getting proper advice and reading up.
Everything will need to be considered for the financial settlement- the house, any other assets, child maintenance costs, household bills for both parties, your incomes, any savings, any pensions, cars.
I hope the website and mediation helps and if you need further advice I'd find a low cost solicitor for an initial meeting.
Good luck!