Note, she does not own the house and is not on the deed or mortgage (and has a poor credit rating so would not get put on the mortgage unfortunately) and as she is not married cannot register a spouse's right over the matrimonial home either.
She might be best advised to get a high paid full time job and buy a property in her name once credit rating sorted out so that she is amassing some property capital before the split as they get on so badly.
If they did split up now then whilst the children are under 18 there may be some right to stay in the husband's home under the Children Act.
On the divorce from the only and first wife who is Japanese in England (not Scotland) finances are sorted out at date of divorce - not - not separation 16 years ago. So probably the Japanese wife would get half the equity in the current house and her husband the other half. The live in partner here has no right to that equity unless she has been paying the mortgage which looks unlikely.
If the male partner were to die without a will then the Japanese spouse gets the first £250k of the estate (and of course her half of the house - in fact if they hold the house as joint tenants (the term has nothing to do with tenancies) then his half automatically goes to her on his death. The man probably has no more than £250k assets here so the children would get nothing. They might then have a right to go to court under a 1975 Act if they are under 18 and make a bit of a claim.
What the man could do now is make a will in favour of his children (even if he won't in favour of his live in partner). Secondly he should as part of the same process "sever the joint tenancy" with his wife so that he can leave his half of the house to whoever he likes - that involves filling in a simple form and sending to the Land Registry. They can buy a will form today and do the Land Registry thing. Those 2 things can be done by Monday if the man will play ball - all that means is his children are protected if he dies. He could also take out a life insurance policy as indeed the poster could to protect her partner if she were to die and she should make a will too - this is not all one way. I was the much higher earner and I am female so let us not be sexist about all this. I would never marry again as I don't want any of my house or assets to go to a partner or spouse, just 100% to the children.
If divorce would mean the Japanese wife is thrown out of the UK then they could go for a judicial separation - used by those who won't divorce on religious grounds but otherwise just as final with financial orders and the like. I think that probably does not have the same immigration implications - an immigration lawyer would be able to advise on that.
If all else fails today's papers are full of attempts by the Japanese to get people to live on their remote islands (4000 islands I think) where populations have halved and neighbouring countries want to take them over!