Basil says:
Chironides whispers some instructions to the Ranger…. "We need to get the others up…go hide. Ill try to distract her long enough so you can slip back inside. Each of those heroes has a powerful healing draught. If we are not too late we can still save them and may yet claim victory"
I interpreted the "go hide. i'll distract her long enough you can slip back inside" as "go inside now while I distract her and hide". This means both he would not be riding you at this time and he would be inside while you are outside. We can retcon this once, but since this is text based clarity is king.
As for breaking through the wall, the DMG isn't very helpful. It mostly just summarizes to "stone has 17 AC and large resilient structures have 27 (5d10) hit points, oh and it might have a damage threshold". A lot of DMs i've heard of use the spell wall of stone to simulate well made stone walls. Under that language, the wall is likely 5 feet thick (to hold such heavy doors) at least and thus has an AC of 15 and 150 hit points (30 * 5). The first option seems a little weak to me, so i'll go with the 2nd.
Assuming you use the warhammer and use extra attack to attack twice per round and deal double damage from the feature of the mason's tools, it would take an average of 4 rounds to break through a section of the wall (42 dmg per round, 150/42 = roughly 3.5). Booming blade does less than extra attack so I'd assume that. Based on how loud that would be, I'd say round 1 she doesn't hear it, round 2 she hears it, round 3 she realizes what that means and probably does something, and round 4 you break through.
Thoughts on both topics?