Dear I'm worried that were going to lose our cottage.... :
Perhaps I might help. Did anything in particular trigger the anxiety of maybe needing to make a move after the baby arrives next March? How long is your lease? It is against the law to discriminate in housing to families with children.
There are local laws, code and rules which do have an impact on crowding in an apartment, but even there a family with two small children are ordinarily not in jeopardy.
You should check with the local government if you have a special reason to believe that your family will be over crowding.
In New York City occupancy standards are controlled by the New York City Housing Maintenance Code:
Sec. 27-2075 Maximum permitted occupancy
a. No dwelling unit shall be occupied by a greater number of persons than is permitted by this section.
1. Every person occupying an apartment in a class A or class B multiple dwelling or in a tenant-occupied apartment in a one- or two-family dwelling shall have a livable area of not less than eighty square feet. The maximum number of persons who may occupy any such apartment shall be determined by dividing the total livable floor area of the apartment by eighty square feet. For every two persons who may lawfully occupy an apartment, one child under four may also reside therein, except that a child under four is permitted in an apartment lawfully occupied by one person. No residual floor area of less than eighty square feet shall be counted in determining the maximum permitted occupancy for such apartment.
The floor area of a kitchen or kitchenette shall be included in measuring the total liveable floor area of an apartment but the floor area for private halls, foyers, bathrooms or water closets shall be excluded.
2. A living room in a rooming unit may be occupied by not more than two persons if it has a minimum floor area not less than one hundred ten square feet in a rooming house, or one hundred thirty square feet in a single room occupancy. ****
d. In any case where the birth of a child or its attainment of the age of four causes the number of persons or children to exceed the maximum occupancy permitted in this section, such excess occupancy shall be permissible until one year after such event.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.