Joint filers are jointly responsible for penalty.
(some background; if you do not carry insurance, you will pay a penalty. Read below about what happens to joint filers when one doesn't carry insurance.)
Ralph and Mary, both age 30, are married and file a joint income tax return. They live and work in Topeka, Kansas. Ralph has minimum essential coverage through an eligible employer-sponsored health insurance plan, but Mary does not have any health insurance coverage. Both are nonexempt individuals (i.e., they do not qualify for any exemptions). Since Mary does not maintain minimum essential coverage, both Ralph and Mary are responsible for Mary's shared responsibility penalty.
So, when you file that joint return with your wife, and she doesn't want to carry coverage because she is young and knows her risk is low, she will still get a penalty. Both of you are responsible to pay it.
ETA: If you claim a dependent, you have to provide insurance for the him, too. If you don't, you pay a penalty. Claiming a dependency exemption is a "facts and circumstances" type of arrangement. That means, if you meet the criteria, you claim him, he cannot claim himself. Under the current rules, if you choose to not claim him, he still is not allowed to claim his own exemption. Hence, YOU will still be required to pay the insurance cost of your kid or you will pay a penalty, if the kid is a dependent, under the criteria of the code. I can imagine all of the parents that don't want to pay will disavow the dependency exemption, and the son that doesn't want to pay either will not want to claim it, as well, to avoid having to pay extra tax. There will be much auditing in this area.