I live in the United States. Is it okay if we chew the gum made from the company Wrigley's, because I hear that it is harm to chew it? Is it okay for my dad to work with a Jewish man; they want to open a store together?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

As for the chewing gum you mentioned in your question, if it contains wine, lard or any other Haram material, it is Haram to chew it. As a rule, it is Halal unless it is proved that it contains something Haram.
So, it is wrong to state that it is Haram due to unproven information. But, it is safer to avoid what is doubtful for the Prophet (Sallallahu Alaihi wa Sallam) said: "Leave that which puts you in doubt and adopt that which does not put you in doubt" [ al-Tirmizi and al-Nasa'i ].
Allah knows best.