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

'brief time' is the definition.
I know nothing about this answer so I cannot judge whether it can be defined by this definition.

'hospital by texan mission holding strong' is the wordplay.
I cannot quite understand how this works, but
'hospital' could be 'h' (abbreviation for hospital) and 'h' is found in the answer.
'strong' could be 'f' (musical symbol for 'forte', 'strong' in Italian) and 'f' is found within the answer.
'mission' could be 'alamo' (famous mission and siege from the Texas revolution) and 'alamo' is found within the remaining letters.
This accounts for all the letters.
This may be the basis of the clue (or it may be nonsense).

'in' acts as a link.

Can you help me to learn more?