He may not want to be tied to you financially, but that's irrelevant. The relevant point is the children. If you can't afford to buy him out, can you afford to pay the mortgage on your own? Also, you need to look at working families tax credits to see if you qualify as a lone parent (I think you will, with two minor children and the earnings you stated). If you cannot afford the mortgage on your own, the tax credits may be the saving grace for you. There is an online calculator I think and Mr Google will help you find it.
Also, you can get a 25% reduction in your council tax, once he has moved out. This will also help your finances.
With regard to the money he gives you for the children, the CMS calculator states that it should be 238.33 per month (based on what you've said he earns and if he's not a hands on dad, he may not have them to stay overnight at all). CMS calculator is here:
www.gov.uk/calculate-your-child-maintenance
As a couple, you may have no option other than a mesher order because the childrens wellbeing will come first. Tackle your finances first - see what you can claim. You may find that actually you can manage financially (I do hope you can) and then be child focussed. You both have a responsibility to keep your children safely housed. If this means you get to stay in the house until the youngest is 18, then that's the best course of action for them.
This is just my opinion. I am not a legal expert, but am going through a rather nasty divorce at the moment and have read humungous amounts of guidance and advice. I believe the above is the starting point for you. Good luck.
p.s. somebody else may say that the starting point is a 50/50 split of the house and then you work from there. However, the welfare of the children will always come first and this is why you should ask for a mesher order if you can. Just because H doesn't want it, that doesn't mean it won't happen. He has no say in the matter if you end up in court.