Touch Screen as Second Monitor - Apps launching on main monitor

You'll need to designate the touch display as your main display to get the behavior you're looking for. Check out this TenForums tutorial, which explains how to do that: Change Main Display in Windows 10 Windows 10. If that doesn't do the trick for you, please post again here and we'll help you get it sorted out.
HTH,
--Ed--

I'm not sure it's a waste of time to keep digging, but it could be time-consuming and difficult. That said, I'd suggest starting out with the items listed in this HelpDeskGeek article "5 Best Software Programs to Manage Dual Monitors" to see if any of them does what you need to have done. I've worked with the first item therein -- namely the free, Open Source (SourceForge) Dual Monitor Tools -- and found it to be quite useful and helpful. I did not, however, have to integrate a (secondary) touch panel into that lineup.
You'll have to dedicate some time and effort to work through these offerings to see if they can handle your requirements. I wish I could shed more light on that for you, but alas, I just don't know.
HTH anyway,
--Ed--

Fraser,

Fraserb82 said:

Does anyone have any experience with using a touch screen as a second monitor ... setup will be extended ...

Yes. I have.

Fraserb82 said:

However, my next problem is that it is launching the applications on my main monitor

Applications launch on the monitor that they were last launched on.
So, just start any application then drag it to the extended monitor & close it while it's there.
It should now keep using the external monitor every time it's launched.

Notes -
- If you ever want to use the application on the computer monitor for a change, just drag it there for the job you want to do and then drag it back to the external monitor afterwards so you can close it there.
- If you ever want to work on the computer monitor alone using applications you have dragged across - disconnect the external monitor first before starting any applications {you probably won't be able to just switch the external monitor off yet leave the cable connected}
- - You can get some add effects otherwise - an application might launch in the non-existent external monitor and you'd have to use WinKey+ArrowKeys to step it back onto the display actually in use.
- - You can do this without disrupting your setting up work. When you reconnect the external monitor, the application that used to be shown on it will be shown there again [your temporary work on the PC alone will not have altered the dragging around you had done before].

Fraserb82 said:

Is there some setting I need to change so that it launches on the second monitor.

No.

Fraserb82 said:

I'm aware we could remove the taskbar, this would then stop the teachers from trying to launch applications direct from the Promethean board and it would get them used to opening the application on their PC and dragging it across.

This might be a red herring - I'm not at all sure about the point you are trying to make here.
It does not matter which Taskbar the application is launched by, the behaviour I have described does not depend on how an application is launched.
- Your comment does make me think you knew this beforehand.
- - Have I misunderstood your question?
- - If so, just what do you want advice about?

EdTittel said:

You'll need to designate the touch display as your main display to get the behavior you're looking for

You do not have to change your main display designation.

Fraserb82 said:

I have managed to get it to use the touch functionality

which prompted

llinfeng said:

I'd like to jump in with a quick note, which did enable touch input on a secondary monitor

Your comment implies that you had some difficulty.
I urge you to report your difficulty to whoever wrote the monitor's instructions. It's the only way they'll learn.


Denis