What doesn't seem to have been mentioned so far is how you own the house.
You can own the house as "joint tenants" where you both equally own the whole house (just like a joint bank account).
Or you can own it as "tenants in common" where you each own a separate and distinct 50%.
If you own the house as joint tenants then the house automatically passes to the surviving spouse regardless of what any will might say.
So, if your DH were to pass away first then you would get everything and it would be quite open to you to get involved with a younger gigolo and then leave everything to your young lover when you eventually pass away so that your children get nothing.
I'm sure that you wouldn't do anything like that but you do read stories on MN about that happening.
Likewise, you could pass away first and then your DH remarries and leaves everything to his new wife. Again, plenty of stories on MN about this as well.
If you own the house as tenants in common then you can leave your 50% share of the house to whoever you like. What normally happens is that your share of the house is left in trust to your children and the surviving spouse is given a lifetime interest to live in the property.
So, if your DH were to pass away first, then you could still give your 50% of the house to your gigolo but you couldn't give your DH's half of the house to him. Likewise if you were to pass away first then it would protect 50% of the house going to any new wife.
Another aspect to consider is that, although relatively few people do actually end up in care, there is always a possibility that one of you might. Owning a house as tenants in common will protect 50% of the house from care fees if one of you ends up going in to care.