You've written that your house is 'in both names' but you've not stated whether you're 'joint tenants' or 'tenants in common'. (Either type of arrangement is possible when two, or more, people co-own property).
If you're joint tenants, neither of you owns any specific portion of the house. It's your legal partnership which owns the house. When one of you dies, the surviving partner automatically acquires the whole of the house. That rule overrides anything which might be written in either of your wills. (Neither of you can leave your 'share' of the house to anyone, since neither of you actually owns a share of the house).
So (assuming that you're joint tenants, which is the more usual arrangement for co-ownership of properties between spouses), your children won't be entitled to any part of the house (or of its value) when one of you dies.
If you and your wife are tenants in common, then each of you owns a specific share in the house. (That share would normally be 50%, unless otherwise specified in the title register for the property). If your wife died first, leaving a will dividing all of her estate between your two children, they would then each have a quarter share of the house. Things could then get rather messy. You could (subject to having the necessary capital) offer to buy out their shares. Otherwise they could seek to force you to sell, but you could apply to the courts to delay any such sale.
So you need to check whether you're joint tenants or tenants in common. If you don't have direct access to the deeds, you can download a copy of the title register, for £4, from the Land Registry:
https://www.landregis...ortal/Property_Search
Chris