I am sorry, I do not have good news. The other parent can place pictures of the children on line without your consent. The person who owns the picture is has the right to use it on line and since they are the other parent they have the right to use it on line.
As far as the behavior no, they should not be putting you down and you can file harassment charges against the parent if he/she continues to do.
DISCLAIMER: Answers from Experts on JustAnswer are not substitutes for the advice of an attorney. JustAnswer is a public forum and questions and responses are not private or confidential or protected by the attorney-client privilege. The Expert above is not your attorney, and the response above is not legal advice. You should not read this response to propose specific action or address specific circumstances, but only to give you a sense of general principles of law that might affect the situation you describe. Application of these general principles to particular circumstances must be done by a lawyer who has spoken with you in confidence, learned all relevant information, and explored various options. Before acting on these general principles, you should hire a lawyer licensed to practice law in the jurisdiction to which your question pertains.
The responses above are from individual Experts, not JustAnswer. The site and services are provided “as is”. To view the verified credential of an Expert, click on the “Verified” symbol in the Expert’s profile. This site is not for emergency questions which should be directed immediately by telephone or in-person to qualified professionals. Please carefully read the Terms of Service (last updated February 8, 2012).