How to use a stirrup pump on kids bikes - no space for chuck?
Sadly no - that short hose would have been used on an old-school frame pump, and yes, it would have been stored in the handle.  The host/pump thread is not the same size or pitch as a schrader.



The threads are not opposites, so that hose won't go into a schrader chuck.

Compare the end with these adapters - see how the brassy one looks like another schrader valve, and the topeak one looks larger?







Your other option is to simply lean the valve stem over a bit, and see if that gives you room to flip the lever.  The valve stem may tear off, more likely if its an old tube.   

Or since its the same as a car tyre, take the bike down to the local service station and use their air bowser to fill the tyre.  Not sure about your location but here most fuel station air pumps would fit fine on any little wheel's valve stem.