The one from the mother should be a letter of invitation rather than non-objection, it's just more of a positive perspective.
Yeah, that's a good point. It's a letter of invitation/permission to stay in their house, not one of non-objection.
A non-objection letter would normally come from an official landlord, where one half of the couple already legally rents the property, and the landlord is saying they have no objection to a second person residing there/being added to the tenancy.
The letter from the mother, in this case, though is much more of an invitation, saying that she is giving both of you permission to stay in the house with her for as long as you need to, and also stating that it won't be overcrowded with you all living there (she needs to state the number of bedrooms + living rooms, and the total number of people in the house).
The father's letter would probably be more of a non-objection letter though, because he no longer lives there and is simply saying he doesn't object to you living in the house that he part-owns.