First and foremost, please provide your residency information. State laws are different and it is different to answer questions without knowing some basic information.
Passport is a federal matter so the regulation is clear. If your child is under 16 and the non-custodial spouse refused to cooperate with the renewal, the only you can do is to get a court order. Whether the court will approve the request, however, is a different matter.
Regarding the weekend schedule, generally speaking, if it is not in your time, you have no right to dictate what the non-custodial parent does or does not do in his time. If he chooses to let the kid stay at home for the entire weekend, this is his right. No court will compel him to take the kid to extracurricular activities in his time. Again, your state law may vary.
