That depends on how the house is registered, if it is as Joint Tenants, it passes directly to the surviving owner, if however it is held as Tenants in Common it passes according to the will.
The normal set up is for it to be held as tenants in common with both parties leaving their share in a will trust for the other with the children as remainderman beneficiaries - that way the surviving partner gets to stay in their home for life, and even if they need care, the deceased partners share is ring fenced for the children.
With a £2mn + estate there is going to be a significant IHT liability whatever you do, there is potentially £1mn of tax free and then 40% of everything else goes to HMRC.