Vil can be will, would and want when translated. When to use will and when to use would has its own rules in English. A plentiful selection of uses too!
On will: (third person sing. pres. t. will) [I] (only used in the simple present tense) (old-fashioned or formal) ); to want or like. "Call it what you will...".
On will, the modal verb, there are plenty of uses (8 in the dictionary) but none that covers this example.
On would, the modal verb, use no. 8 (out of 14): used in polite offers or invitations. "Would you like a sandwich?"
Hvil is a rest, or the imperative of to rest. It is pronounced with a drawn out i.
Vil means both will/would (and want). It is pronounced with a short i, exactly the same way as vill, "wild", but it is not difficult to tell them apart in a sentence. Ville is both the verb will and the plural form of wild.
Ta deg en hvil = Get some rest. En vill hund = A wild dog. Barna vil ikke = The children don't want to. Han er vill = He is wild. Jeg vil hvile = I want to rest. Jeg ville hvile = I wanted to rest. De ville dyrene tar seg en hvil = The wild animals are getting a rest.