lots of relationships have escalated over the internet. it's no different than if she ran into some random guy at the supermarket and started developing a close friendship with him. She should be focusing on your relationship and building that and making it stronger.
I have said no and have tried to implement the subjection issue which is a little shaky at the moment.
Don't do that. Absolutely the wrong way to go with this, it will almost certainly cause her to want to do it more out of spite. You own her and can't make her do anything she has to want to and if she doesn't see you are threatened by this and that alone makes her want to stop then there are other issues at hand.