"The ambulance took my husband to the hospital."
Translation:Thóg an t-otharcharr m'fhear céile chuig an ospidéal.
Why is it wrong "Thóg an t-otharcharr m'fhear céile go dtí an t-ospidéal"?
Because of the preposition chuig. Like other prepositions, chuig + an would normally cause eclipsis, but in the case of nouns that start with a vowel, you just get the plain, unmodified word, without the t-prefix that ospidéal would get in the nominative case after an.
Yes it would - go dtí is a little bit odd, in that it doesn't trigger the dative (as the simple prepositions do) or the genitive (as many of the compound prepositions do).
In a previous discussion you may have read that go dtí is used before the definite article instead of just go.
go hospidéal - "to a hospital"
go dtí an t-ospidéal - "to the hospital"
(go hospidéal is just for illustration - it isn't really used much in my experience).
Whether you choose to use chuig rather than go / go dtí has nothing to do with whether or not the noun is definite.
chuig ospidéal - "to a hospital"
chuig an ospidéal - "to the hospital"