Does returning from a deployment change your time on station?

No it doesn't and your BM probably just got something mixed up. If you did only have 3 months on station then you would not have PCS orders.
But, you are already on assignment and your branch cannot easily remove you from that. If your branch has already fulfilled it's recruiting mission oh, they cannot place you on a recruiting assignment. You would need to submit your recruiting packet directly to recruiting branch. instructor positions are assigned under the normal assignment procedure. That means that there was a greater need for you to go where your orders are currently taking you, then there is for you to be an instructor.
You are not a high priority for broadening assignment because you are still only a sergeant. Even if you are promotable, you still need time in a staff sergeant position before a broadening assignment he comes a critical factor for you. There are other staff Sergeants in your MOS who require a broadening assignment more than you do in order to be competitive for promotion to Sergeant First Class. That means that you will be the lowest priority for a broadening assignment in your MOS

Yes it will reset your overall dwell time