Hello and thanks for using Just Answer.
My name is ***** ***** am happy to assist you with your enquiry.
You are quite correct in that your daughter in law is NOT able to register any such Home Rights Notice as any such Notice can only be registered if one of the spouses owns the property, which is not the case here.
She did of course have rights of occupation under any "tenancy agreement" she had with you, but I note she has since vacated.
As regards ***** ***** interest she may have, such an interest only arises if a party has spent money on improving a property. So, for example, if she has spent £x
fititng a new kitchen or adding a Conservatory, she has acquired a beneficial interest based on the increase in value this addition has given to the house.
The mere payment of rent or other household bills does NOT creat any type of beneficial interest at all, and nor does her mere past presence in the property.
I hope this assists and set sout the legal position to you.