I don't railroad.
And there's only so much railroading can do to stop a clusterfrak like this, short of Deus Ex Machina or--worse--fudging rolls.
To the first bit - that's no good. You need a little bit of railroading if you want to get a campaign going. To actually put the PCs on the rails to begin with rather than just plop them into a situation and going 'do whatever, man'. The thinking that railroading is akin to dictatorship and you should not do it ever is asinine to say the least.
To the second one, you didn't actually need to railroad too much. Just have the place we were at have, you know, guards. And secured gates you can't just run away through. And have the prince and the other lady do something other than say 'that is most displeasing, hrm'. From a story point of view, it would make sense, considering that this is some kind of military operation and that it has decided to host a whole bunch of unstable, dangerous weirdos (apparently engage in 'basic training', too).
Tell that to every GM I've ever played under. Start with piecewise, I'm sure the HMRC* would appreciate it.
*Yes, I know they're ARM now. Shut up.
Distinction: piecewise's overshoots are often funny or impressive (description counts for a lot, you see) rather than simply disruptive or annoying. And they fit with the tone of the game itself, unlike here. Notice the spoiler above the original intro to ER stating both "Incredibly fatal" and "Black Comedy". And I
still think they sometimes tend to detract from the game (not to mention screw over character progression to the point where you need a highly expensive item to be of any use whatsoever after reaching a certain skill level).
Also, I'm technically a GM you once played under, and I support the message of overshots not needing to be 1 levels of bad, or even as bad as a 2.