I see you have not had a reply, so I will try and give you a few pointers.
The first and most important issue is, how are you both going to be re-housed, and especially the children.
In your case, both of you earn a reasonable wage and there is a lot of equity. Ideally you should have a house big enough to enable you to have the children stay with you.
There is no doubt at all that your wife needs to have a re-assessment of her benefit entitlement , especially tax credits.
There is no law in England and Wales that inherited property is retained by the spouse who inherited it. But certainly it is a consideration, firstly that you inherited the money and used it to finance the purchase of the marital home.
The options that you have ( by which I mean the realistic ones ) are
1. Sell the property divide the proceeds and each of you buy a property of your own.
2. Either of you buys the other out, if it can be afforded.
3. The parent with care will have the right to live in the house for the time being, usually till the children have grown up. The house will have to be sold at some stage, typically,
· Death of the occupying spouse
· Re-marriage of the occupying spouse
· ( Possibly ) cohabitation of the occupying spouse for a period, say, 12 months. This is perhaps somewhat controversial ; the argument being that the children still need a home even if Mum gets herself a new boyfriend, and that consideration outweighs the non-occupying spouse’s need for cash.
· The youngest dependent child reaching the age of 18 years or ( possibly ) completing a first undergraduate degree.
· Voluntary vacation of the property for a given period.
· Sale of the property. However, a well drafted order should make provision for the possibility of the occupying spouse moving home and the new home is then held on similar terms.
Triggering events are a matter for negotiation but the above are the most usual. This list does not purport to be exhaustive.
However the marital home, though important, may not be the only asset. There are others and particularly pensions. Your wife will have a pension, do you have one ? What other assets are there ?
I don''t like to advise people about housing options because so much depends on where you live.
But, as I say, this is a start.