Your dilemma is understandable. On one side you have your girlfriend who doesn't trust you, and on the other side you have your own family. Though it appears like a no win situation, you should not lose hope. Uncertainty and indecisiveness is what harbours anxiety
If you are well settled (professionally), then you should take a positive decision and stick to it. Things will fall into place automatically. In case you are not settled well, then it is advisable to take some time to decide. Till then, you should make it clear to both your girlfriend and family that you are not abandoning them, but only postponing the issue as you cannot concentrate on your present career buidling. Be calm and composed when dealing with others' insecurities.