TD, screw the Hawker that's BEHIND you. I hope by "keep the speed up" you mean maintain normal approach speed and not fly a faster approach. If not, then you seem to have issues with stabilized approaches. Yes, you pose a real world situation. Flying a faster approach is not a real world solution. Flying a normal approach speed is a real world solution...actually, procedure. Sure, you hear 121 guys being instructed by ATC to maintain best forward speed or XXX kts to the marker. All that ends at the outer marker; inside the OM (or whatever the appch has) it's up to the pilots to fly Vref or be slowing to it. Depending on VMC or IMC the approach has to be stabilized by a certain altitude (usually 500' or 1000' respectively).

Let the Hawker worry about what to do. All you can do is state your position and intentions and allow the Hawker pilots to adjust. You are in a more critical phase of flight and they are more maneuverable. Sure, I could add that they should have called prior to 4NM, but I know that it happens.

Just make sure you don't get your students thinking that jets have priority (although, we'd like to have it) and that they need to rush a critical maneuver (landing) to satisfy others. Plus, your student is paying to fly that 172. Those Hawker boys are getting paid to fly and a go around isn't cash out of their pockets.

Regarding the confusing clearance, call the ATC facility you were talking to. Tell them the date, time, location, altitude you were at and maybe the controller will be available to discuss the clearance with you. If not, maybe he will be able to get back to you or another controller/supervisor may be able to help. Controllers are friendly and like to hear from pilots.