yes, i would explain where everyone sleeps and take pictures of the rooms, but it would have also been better if you had the independent report, but like you've said you've no time now..

but i think they should not say the house is over crowded if you get pictures of the rooms and size and where everyone sleeps but without the report i still hope not.

maybe you could send a list of options you have.

you and your husband in 1 room with your youngest
your older daughter in the 'double bedroom' with your mom sharing 2 * single beds
your son in the single room

another one of the options is.

you and your husband in 1 bedroom
the bunkbed in the other 'double bedroom' with both your daughters sharing the bunkbeds and your mom in the single bed.
and your son in a single bed in the single bedroom. - bit crowded with 3 people in one room thou.

or as you've said your mom could sleep in the living room