First, keep in mind that there's no direct correspondence between prepositions; you have to look at the exact meaning and figure out which preposition is the best match. (This is true of most words in fact, but prepositions are often particularly tricky in this respect.)
German allows you to drop the main verb when there is a modal verb (such as müssen) and there is a preposition which makes it clear what movement is meant. This is why Aus diesem Grund muss ich oft mit ihr ins Krankenhaus. doesn't appear to have a main verb, even though müssen would normally require one. This isn't allowed in English, even it means using a filler verb like "get".
Note also that you're using "visit" in an unusual way here. Normally you "visit" a person, go to where they live or work, talk to them a while, and then leave. You're not doing this with the hospital; presumably it's someone inside you're actually "visiting". English allows this as another meaning, but you should not assume that these secondary meanings carry over into another language, and even if they do, that it would be the most natural way of expressing the intended meaning. In this case I don't think the meaning does carry over. (There is a secondary meaning of besuchen, but its best translation in English is "attend". So really the meanings of "visit" and besuchen just have a certain amount of overlap; they aren't an exact match.) I don't know the exact context here so it's hard to tell what would be the best verb to use. You could go with a generic kommen or, since it's allowed in this case, drop the verb altogether as the automatic translator has done. (Note, DeepL uses besuchen but I don't think this is correct. DeepL may be thinking you have the main meaning of "visit" in mind, which doesn't make sense to a human but DeepL is just an AI enhanced computer algorithm.)
You also need to think about what you're going to do when you get to the hospital. I assume you're going to go inside and not just stand in the parking lot for a while. So it makes sense to use ins. English allows "to" since the "in" is implied, and especially since "in the hospital" implies you're sick and not just in the building. German, however, seems to prefer you to be more specific. But prepositions are rarely that easy to pin down and there are exceptions. With locations the size of a city or larger you'd normally use nach rather than in: Ich fahre nach London. But an exception to this is exception is any location with an article, in which case you revert back to in: Ich gehe in die Vereinigten Staaten.