It depends on the local laws. News reporters very often push the limits and it would do them good to get their fingers burnt, but it's a huge amount of stress and financial risk to take action and follow through. Usually there's nothing you can do about them showing up in a public place. You can prevent them entering your own private property (but not someone else's). In some places anti-stalking laws or privacy laws could apply, but probably only if it went on and on.
In some nations the act of publishing theoretically confers copyright protection, but in others you have to take further steps. It is even more complicated on the Net when you may post something in one country but the server may be in another. In such cases it's often in practice next to impossible to enforce copyright laws.
You should never assume that the news media will respect your wishes in any matter, even if they promise you they will. Such promises are easily given, but are usually broken. In cases like this, reporters have often been known to steal family pictures from the house.