Is the money spent by a Christian American family on a Muslim refugee considered unlawful (haram), knowing that they own a company and invest their money in a non-Islamic way?

It is permissible for you to take money from these people, even if they engage in illicit dealings. The Messenger of Allah, peace and blessings be upon him, accepted gifts from disbelievers despite their engaging in usury and other forbidden acts. Therefore, as long as a Muslim does not know that the money itself is from an illicit source, there is no harm in taking it. However, one must be cautious not to incline towards their beliefs, be influenced by their customs that contradict Islam, or be alone with their women, or look at their awrah (private parts).