So my wife and I just started our first game and her mission card was to go to the Apothecarium Sepha…. She was the Adepta Sororitas and so started on St. Antias sanctuary. For her movement phase can she just spend the 2 influence to go up a tier?
Seems like you could…. Then can use the recover option even though she doesn't need it and complete her mission correct? On her next turn can she just exit the same way she came in? Does she even have to spend influence?
or is it a one way trip for her and she should ignore the mission and just run around the outside for awhile before going in?
First off, you can't use the text from any of the outer tier corners at the start of your movement, they are done when you do your Engagement Phase is the space (assuming there is no card there), so even if you start in a corner that can move a player to the middle, you have to move to another space and either come back to the original space another turn or go up from another space (roll a 6 gets you to another corner).
Second, this is exactly why you can't do anything on the middle tier after you use a corner, because all the move to middle tier options say "then end your Engagement Phase", meaning you don't get to use the ability of the space you move to on the middle tier that turn.
Barring special movement abilities (like Nyphoma Astrolabe Relic), only way to get from the outer tier back to the middle tier is to use the Space Hulk to spend 1 movement point to move to the Webway Portal (or get vanquished). Note that Space Hulk and Guardian of the Rift spaces are movement boxes that allow you to use their text during movement, as specified in the rules.