"אם תרצי אני אלך הביתה."
Translation:If you want I will go home.
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So am I correct that תרצי in this sentence is not functioning as a future, but in a modal way in conjunction with אם? I.e., the אם signals some measure of doubt that the envisioned condition (viz., the addressee wanting) is true, which calls for the imperfect/future. I.e., the imperfect is used here not with reference to a future time, but in a modal way. Is that right?
No, you can't. And here's why: The Hebrew syntax here is one of two ways of saying "to the place/direction" - in this case, "the place" is "the house / the home" = "הבית", pronounced "ha-ba-it". At least in the case of "הבית", the actual meaning is different between the two ways, but more on that later. The way used here is "הביתה", pronounced "ha-bai-ta". The other way is "לבית", pronounced "la-ba-it".
So, for your question, "לביתה" is an incorrect mix up, and not a word at all, even outside the scope of this sentence. But I suggest reading on for some notes on usage (which explain why you also can't use "לבית" here).
The first way ("הביתה") is used for "home", as in "go home" ("I'm going home", "go home!", "don't you want to go home?"), almost exclusively.
The second way ("לבית") is used either for 1) "to the house" 2) "to the home [of someone]"/"to [someone's] home", where "לבית" is followed by "[של מישהו]". It can be "my/your/their/..." instead of "[someone's]" by using the proper inflection of "של".
So, while technically, "go home" and "go to your home" mean the same thing, it's more accurate to translate "go home" to "לכי הביתה", and "go to your home" to "לכי לבית שלך". *The Hebrew translations in this paragraph assume you're speaking to a single female person, for no particular reason.