No parent is ever a "part-time parent", whether or not the child live under his/her roof or not. Viewing the non-custodial parent as a "part-time" suggests believing that parenting is only about making sure children are fed, clean, and "babysat".
The term, "biological parent", suggests adoption. In an adoption situation the biological parent is not the child's parent at all. The person who legally adopted the child is the parent. There is no "part-time" and "full-time" there either.
Respectfully, the wording of this question seems to attempt to diminish the significance/role of the non-custodial parent. This assumes that the non-custodial parent has nothing that makes him an unfit or abusive parent.
The ideal situation is for both parents to agree to a generous visiting plan with which both are comfortable, and then have that established in a court order. Not having these arrangements agreed upon in a court order can leave too much room for misunderstandings and inconvenience. On the one hand, a non-custodial parent shouldn't be expected to just "pop in" whenever he feels like it. On the other, being a parent is inconvenient. Custodial parents share their children with the non-custodial parents, and it can be unreasonable to expect never to be inconvenienced.
Without knowing the exact circumstances, it's difficult to be specific about "where to draw the line". The best thing would be to work something out amicably (if possible) in court, and follow the court order. That way there isn't any room for worrying about how flexible anyone needs to be.