DO NOT SIGN. Not yet, anyways.
I assume he is still named on the mortgage, and therefore liable.
In that case: immediately stop paying the mortgage yourself and inform your lender of the situation.
(As soon as he stopped paying you should have informed your lender that your ex refuses to pay the mortgage and has not contributed since [date]. )
If you did not already inform them, you should update them on the situation now.
If you already explained the situation to your lender, call again and reiterate you are separated frim your partner and he is financially abusive. Tell them you have run out of money to pay his contributions as well as your own, that he is still refusing to pay because he wants to try and financially ruin you by starving you and the children out of the house, as he thinks this will force you to agree to a settlement settlement that leaves you with almost nothing and him with no responsibility to pay maintenance (mention he is self-employed and lies about his income to avoid CSA). Ask your lender for a hardship stoppage so that you get a break from mortgage repayments. Make that as long as you can - 3 months or 6 months if possible.
THEN you get solicitor to write letter to mediator and ex's solicitor saying, you have arranged a mortgage holiday and you will not be blackmailed into reducing the divorce settlement at the 11th hour. In fact, your ex's aggressive demands have made you realise you are being financially abused by your ex and you believe you are settling for too little, and so you want to go BACK to mediation. In the letter mention make sure you mention the amount of mortgage contribution unpaid by your ex as his share should be taken out of the final settlement and given back to you. Also in the letter mention that when the mortgage holiday ends on [DATE] you will not make any further payments due to the length of time Ex is taking to reach a reasonable settlement. CALL HiS BLUFF. If neither of you pay the mortgage BOTH your credit ratings will be ruined and that will be to his detriment, possibly more so if he is self-employed. It takes a while to repossess a house. And there are costs that he will have to share. I'd let it go right to the wire, personally. Don't let him win.
Meantime ask your lender if you can kick off steps to convert to an interest-only mortgage. If they say Yes it is possible, you can document these steps you are taking. Your ex will obviously refuse to agree to sign an interest-only mortgage as it would extend the amount of time you can afford to stay in the house and hold out on the unfair divorce settlement. But by taking steps to TRY to arrange an affordable mortgage, you can show the mediator AND your lender you have been very reasonable: you paid the whole mortgage when he stopped; you kept the Lender informed; you sought means to make the mortgage affordable by going interest-only (which we expect he'll refuse to agree to as he knows it will mean you can stay in the house and hold out on the divorce settlement).
At THAT point, you get your solicitor to write back to Ex and Mediator outlining how reasonable you have been, and how ex has frustrated your efforts, financially abused you by refusing to pay his share of mortgage or arrange a more affordable mortgage, and tried to blackmail you into a worst settlement after the mediation.
The absolute key to this is informing the lender at every step. They could be very helpful, I expect. There also situations where you can apply for a court order to remove partner from the deeds of a property, your solicitor could advise on this, if all other steps have been exhausted.