Simple answer: Your H4 Status is a dependent status of H1B. As long as H1B is valid, your H4 is valid. Now, traveling in AP through TPS, your H4 status is NOT voilated. You can travel anywhere, but the question is will you be able to re-enter US with AP ? The answer is 'Nobody knows' as AP does not guarantee you to re-enter at POE. Decision is entirely at the discretion of the officer at the airport to allow you or deny re-entry (which is again based on your immigration status and history). Note that every case is different. If someone has no problem re-entering the US with AP, that does not mean its application to all. So, like I said, please consult lawyer before leaving US. As far is your question of H4 gets voilated, it will not be violated. Once TPS is expired, you will be back into your H4 status (provided H1B is valid). Hope that answer you question.