keesio said:
Yes, they want all (non-Canadian) children listed. It doesn't matter if she has custody or not. They must be listed and they want medicals for them.
This depends on the age of the daughter. Right now (definitions are changing in 2014), "dependent" is defined as:
-is under the age of 22 and does not have a spouse or common-law partner;
-is over the age of 22 and has been continuously enrolled as a full-time student and depended substantially on the financial support of a parent since before the age of 22;
-became a spouse or a common-law partner before the age of 22 and has been continuously enrolled as a full-time student and depended substantially on the financial support of a parent since becoming a spouse or common-law partner, or
-is over the age of 22 and depended substantially on the financial support of a parent since before the age of 22 because of a physical or mental condition.
If the daughter is currently under 22 or falls under any of these, she needs to be listed as a non-accompanying dependent, and CIC will want her to get a full medical done. This will keep her eligible to sponsor under family class in the future, should she ever wish to. Even though she is currently under custody of her dad, situations change.
If she doesn't do a medical exam, she would be barred forever as ineligible under family class. CIC will sometimes allow this to happen, but usually they want the applicant to sign an affidavit that they understand and accept that not doing the medical for their dependent at this point will forever ban them from getting PR under family class in the future.