This can be difficult for the beginner without Tips and Notes. चाहिए means 'is wanted/needed' from the verb चाहना, to want. I think it takes the Dative and these unusual forms: तू + को > तुझे; मैं + को > मुझको or मुझे. Am I right?
Could this also be translated as "You and I would like mangoes"? It sounds really rude in English to go around saying "I want this. I want that." "Would like" is much more polite, especially if it's in the context of making a request.
It is better to keep to the literal translation of the verb at this time. There is no conditional aspect to this sentence.
And what is wrong with using "मेरे और तेरे"? How come "मेरे" was used as "my" and "I/me" before? I am really confused at this point. Please bring the tips and notes :(
As a native speaker, I can tell you that "मेरे" means "mine (plural)" and "तेरे means yours (also plural)". Thus, it wouldn't make sense to say "Mine and yours want mangoes", so we use मुझे and तुझे. This can be a bit confusing as मुझे and तुझे can be used in many different situations, like "मझे वह चहिए" or "I want that", but it is usually associated with the verb "to want". I hope this made things a bit clearer.
In the first comment, it's pointed out that this pronouns are in the dative case.
Clearly, the translation is wrong. Chahie is totally different from "Chahiyen". Please, do report it.