I was just looking for some clarification.

Lady mentions:

" Action: Pay 1 gold to attach Lady to a different character. Then, if attached character is Sansa Stark, stand her. (Limit once per phase.)"

We went under the assumption that this meant the entire action can only occur once per phase. While it could possibly mean that Sansa can only stand from this once per phase, we didn't believe it was limited to the last sentence alone. Are we correct in making this assumption?

Yes. The limit is on how many times the entire Action can be triggered, not on how many times any part of it can resolve.

This thread discusses it in detail.