If you really want to write the reaction for sulfuric acid and "ammonium hydroxide", then it would look like this:
NH3(aq) + H2SO4(aq) --> (NH4)2SO4(aq)
And it would be **even better** to write it as the ionic equation, since some of these species only exist as ions in solution.
NH3(aq) + H+ + HSO4- --> 2NH4+ + SO4^2-
Sulfuric acid is a strong acid only for the first hydrogen ion that comes off. It leaves the weak acid HSO4- in solution.