I would just repeat what all the other pp's have said.
At the end of the day, it is entirely down to you how you wish to leave your estate.
If you own your home as 'joint tenants' then you each jointly own the whole home (just like with a joint bank account) and the house will go to the surviving spouse regardless of what any will says.
If you change the ownership to 'tenants in common' then you each own a separate 50% of the home and you can leave your own 50% to whoever you like.
So, for example, you may choose to leave your 50% to your children. It would also be wise to make a provision that your DH can remain living in the home if he survives you.
Likewise, your DH can choose to leave his 50% to whoever he likes. How he splits his estate between his children with you and his children from his previous marriage is entirely up to him. But a will can be written to accomplish any sort of split that he might come up with.
Again, it would be wise to include a provision that you can remain living in the home if you survive him.
If you are unhappy with the person who wrote this will then you may wish to speak to another solicitor. There is a body called the Society of Trust and Estate Practitioners (STEP). These are solicitors who have a lot of experience of dealing with wills and related issues, just like yours.
If you search something like "STEP solicitor [name of your town]" then that will provide a list of local STEP qualified solititors local to you.