Brief time in hospital by Texan mission, holding strong (4,1,2)

'brief time' is the definition.
I don't know anything about this answer so I can't judge whether this works.

'hospital by texan mission holding strong' is the wordplay.
I cannot really understand how this works, but
'hospital' could be 'h' (abbreviation for hospital on maps) and 'h' is found within the answer.
'strong' could be 'f' (musical symbol for 'forte', 'strong' in Italian) and 'f' is found in the answer.
'mission' could be 'alamo' (famous mission and siege from the Texas revolution) and 'alamo' is found within the leftover letters.
This accounts for all the letters.
This explanation may well be incorrect...

'in' acts as a link.

Can you help me to learn more?