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It depends on how you hold your interests in the property. You can either hold your interests as joint tenants (in which case a deceased's persons share passes automatically upon death to the survivor regardless of any direction in the deceased's Will) or as tenants in common (in which case a deceased's persons share passes according their Will). You conveyacer will ask how you want to hold your interests. If your partner's interest was to pass to you upon your partners death then the children it will be very unlikely that her children could force the sale of the property.
If you hold as tenants in common and your partner were to die then her share would pass to her children under her Will. They could make an application to Court for an order of sale of the property to realise the equity in the property. These orders are seldom refused.
You would have to negotiate how the equity is divided unless there any any express agreements. Your solicitor will likely ask if you are to hold your interests 50/50, if you are not then they will recommend you entering in to a declaration of trust which declares the proportion of your respective interests. This will then be used as a reference in deciding how to divide the proceeds of sale (if you were forced to sell the property).
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