To answer that specific question - it depends.
The first question to start off with is - who owns the house?
Is it owned solely by your mum? Or is it owned jointly between as joint owners?
This is very important.
Most homes are owned by a couple as "joint tenants". This is where you both jointly own the whole house (just like a joint bank account). So, when one of you passes away the house automatically goes to the surviving spouse.
(This is the English terminology, if you're in Scotland then it will be something like "survivorship destination")
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 mum were to pass away first then he would get the whole house regardless of what any will says.
The other way for a couple to own a home is as "tenants in common". In this situation you each own a separate 50% of the home and you can leave your own 50% to whoever you like. In this situation it is usual for each spouse to leave their 50% to their children (but you can leave it to whoever you like).
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That's the situation if your mum and her husband own the house jointly.
If your mum owns the house just in her own name then it's a different story.
So, the first thing I would suggest is to go to the HM Land Registry website and download the title register for your mum's home. This will cost £7 and you need the address and post code.
https://www.gov.uk/search-property-information-land-registry
This will either show the registered owner as just your mum or it will show that both her and her husband are the registered owners.
If they are both registered owners then you need to find out if they own it as "joint tenants" or as "tenants in common".
You can do this by looking at the title register. If there is a restriction that is worded like this:
"RESTRICTION: No disposition by a sole proprietor
of the registered estate (except a trust
corporation) under which capital money arises is to
be registered unless authorised by an order of the
court"
Then the home is held as "tenants in common", and they each own 50%. If there is no restriction like that then they own it as "joint tenants" and everything goes to her husband after she passes away.
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What you do next depends on whether your mum is the sole owner of the house or owns it jointly either as joint tenants or tenants in common with her husband.
If she goes to a solicitor who is used to dealing with wills then this will be a straightforward matter to sort out.
Depending on the situation, if your mum owns the house on her own then it is likely that the will, will then say that the house is left to the grandchildren in trust on her death and that you will be a trustee.
It will also likely say that her husband has the right to live in the house until he dies or some other event happens. This other event may be something like co-habiting, remarriage or moving abroad etc.
In that situation, he may be able to bring a claim against the estate but that is something you need to talk to a solicitor about. If the will just left everything to the grandchildren and kicked him out of the house then he might well have a claim in that situation.
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In contrast, if the house is owned jointly then the first step is to get that changed to tenants in common if it is not already like that.
If the house is owned as joint tenants then he will get the whole house after your mum dies.
Once the house is owned as tenants in common (your mum can do this herself or a solicitor will explain how to do it) then your mum and him each own a separate 50% of the house.
In this case, she can leave her 50% of the house to her grandchildren but her husband does own the other half.
In that situation, the usual advice is to put your mum's 50% share of the house into trust in the will so that the beneficiaries (the grandchildren in this case) cannot kick the surviving spouse out of the house. But do I get the impression that you wouldn't mind if he moved out?
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So, it all depends on the ownership of the house. If it's just in your mum's name then she can write her will however she likes and leave everything to her grandchildren.
If her husband is also a joint owner of the house, then there's no getting away from the fact that he is going to end up with 50% of the house.
But, as others have said, you need to tell all this to a solicitor and they will write a will that achieves what you want to happen.