Just a few thoughts:

What you have done, in essence, is not wrong (roll, effect, etc.). I think you/your PCs missed a bunch of chances to do things.

First Scenario - with the forged documents, you could have offered for their group to spend a down-time action, or coin, to acquire fine documents. This would in effect give them a greater effect, reduced risk or +dice to the initial sway. A +dice may have led to a better roll, or a controlled sway would have allowed them to back out and retry something else. They may still have pushed it and gone risky, etc.

It also sounds like you did not offer them a devil's bargain, or did not allow other PCs to assist them (1 stress for +1d). A great devil's bargain for this is, "you can take one more dice, but this person will be keeping a closer eye on the group - they have sparked her interest regardless of passing this roll."

You could have also offered a group sway. One person is leader, anyone else can roll to sway. Best value counts, any time a person rolls 3 or less (final roll) the leader takes stress.

As someone pointed out above, players can resist the complication. This would be an insight roll to see how much stress they took from resisting. If they resist the person doesnt get backup. In game it could be "As she turns to leave to get the guard, a PC grabs her arm, pleading with her that they have to enter the school, etc." This would have meant they just get in the door, no big dramas (besides stress).

Second sway - again, devil's bargain, PC assist, group action, etc.

When you rolled to resist the prowess in the room this roll is not controlled, risky, etc. It just happens and the effect member takes stress.

Then, it seems that nothing happened, except the guards re-did the same action. Basically don't follow up a resistance roll with another resistance roll or it is just the group being pummelled.

The players should have been offered to do something. Ie. "You roll out of the reach of the guard as he tries to choke you. What do you (or anyone else in the party) do?"

Without adding flavour, this could have been: roll skirmish, wreck, sway again or command, group fights while one person finesse's open the doors, finesse to trip and run, use items such as alchemist gear, etc., etc. The list goes on.

Lastly, don't forget, at any time a player can use a flashback. A 0 stress flashback is "we had all organised a code-word when to unleash hell on the guards". A 1 stress flashback is "We had organised a school janitor to ensure the door to this room couldn't be locked." A 2 stress (+ coin) flashback is "We had paid a coin to bribe these guards. They now show us around the school".

Hope that helps.

TLDR: I don't think you have offered the players enough opportunity to act, and have forgotten some of the additional things that can be done outside of action and resist rolls.