FIrstly, there is no such legal term as a "mother-daughter". A "mother-daughter" house is, essentially, a legal one family house together with an illegal apartment. Building Department Inspectors are entrusted with investigating illegal conditions. Do you have to let them in? No you do not. You will then likely be cited with a violation for "failure to provide access". An Inspector may procure a search warrant if they choose to do so, but they normally will go that route only if it appears that a condition exists that presents a risk to person or property. Whetehr you changed it is really not the issue. The issue is whether someone who preceded you changed the house and did so without the approval of the Department of Buildings. Rather than a lawyer, it would seem that you really need to engage an architect.
The way it was sold to you has no bearing on whether it is legal or not. It was common practice 20 years ago to build what amounted to illegal apartments and sell them. It is likely that the original building plans did not include the apartment and even though you are being taxed as a two family, the certificate of occupancy was probably issued as a one family dwelling with garage. This amounts to an illegal garage conversion. You would either have to get a permit to convert it to a legal 2 family dwelling, or get a mother daughter permit if a family member is living in the space or return it to a garage.
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