1) I am a new Muslim. Can I show my hair and arms to my male cousins, my mom's sister's sons? Can my husband shake my aunt's hand and give her a hug? Please verify your answer with evidence from the Qur'an or authentic Hadith.2) I am the only one in my family who is Muslim, and my parents want us (my husband, daughter, and I) to stay here in the United States to live and my husband's family wants us to go back to his Muslim country. What is the best thing for us to do? I have been very undecided what to do because my mom makes me feel guilty about leaving her because I am her only daughter and I have two brothers. 3) Can a man shave his chest hair? Is there any authentic Hadith about this?

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.

A woman is not allowed to uncover her hair, arms or any part of her 'Awrah (all woman's body is an 'Awrah) in front of others except unmarriageable men and her husband, whatever their relation is with her.
Allah Says (interpretation of meaning): {…and not to show off their adornment except only that which is apparent (like palms of hands or one eye or both eyes for necessity to see the way, or outer dress like veil, gloves, head-cover, apron, etc.), and to draw their veils all over Juyubihinna (i.e. their bodies, faces, necks and bosoms, etc.) and not to reveal their adornment except to their husbands, their fathers, their husband's fathers, their sons, their husband's sons, their brothers or their brother's sons, or their sister's sons, or their (Muslim) women (i.e. their sisters in Islâm), or the (female) slaves whom their right hands possess, or old male servants who lack vigour, or small children who have no sense of the shame of sex.…} [24:31].
In addition, cousins are not Mahaarem (unmarriageable people) so you are not allowed to uncover your 'Awrah in front of them.
In a Hadith reported from 'Aqbah Ibn 'Aamer that Allah's Messenger (Sallallahu Alaihi wa Sallam) said: "Avoid visiting alien women. A man from among the Ansar (the Prophet's (Sallallahu Alaihi wa Sallam) companions of al-Medina) asked: 'O Allah's Messenger! What about husband's brothers or in-laws?' He (Sallallahu Alaihi wa Sallam) said: 'These are death" . [Reported by Imams Bukhari and Muslim ]
This Hadith clarifies that you are strongly required to avoid mixing with such a person, whether you are a new Muslim woman or an old one. In other words, such an action is Haram for all Muslims, without any distinction between new and old, poor and rich Muslims.
Also, a husband is not permitted to shake hands with his wife's aunt or to hug her, since she is not from among the everlasting Mahaarem. In simple words, she is temporarily prohibited due to his marriage with the daughter of her brother or daughter of her sister.
If a husband orders his wife to travel with him to some country, she has to obey him, and his obedience is given precedence over parents' obedience in the Islamic Sharia.
However, we have to treat parents kindly even though they are non-Muslims.
Furthermore, we fear for you and your husband living in a non-Muslim country, in the west and other countries where one cannot live according to Islam Day by day all the family will become weak in faith. You have to move to some Muslim country or a country that does not prevent you from practicing your religion. This action will be considered, Insha Allah, a form of Hajirah (migration) for the sake of Allah, His religion and to save faith.
Anyone who leaves something for Allah's sake, He will give in exchange for that what is better.
Allah knows best.