Her relative works in a haram job and gave her some money as a gift

Praise be to Allah.

Firstly: 

haram wealth is of two types: that which is haram in and of itself, such as wealth that has been stolen or seized by force. It is not permissible to accept this from anyone, because it must be returned to its owner. 

(The second type is) that which is haram because of the way in which it has been acquired, such as money that is taken by means of dealing in riba or doing haram actions, such as bribes, cheating and payments for singing and dancing. That also includes what you have mentioned of working as a sound engineer for haram movies and soap operas. This wealth which is haram because of the way in which it was acquired is haram only for the one who acquires it. As for the one who takes it from him by permissible means, there is nothing wrong with that, although it is better to refrain from taking it and to err on the side of caution and not benefit from it, especially if not taking it will affect its original owner and make him give up this work. 

It was narrated in a saheeh report from ‘Abd-Allah ibn Mas’ood (may Allah be pleased with him) that he was asked about a person who had a neighbour who consumed riba and invited him to eat with him. 

He said: Accept his invitation, for the pleasure will be yours and the burden of sin will be his. End quote. Jaami’ al-‘Uloom wa’l-Hukam (71). 

Shaykh Ibn ‘Uthaymeen (Allah have mercy on him) was asked: A man knows that the source of his father's wealth is haram; can he eat his father’s food? If he does not eat his father's food, is that considered disobedience to his father? 

He replied: With regard to the man who knows that his father's wealth is haram, if it is haram in and of itself, in the sense that he knows that his father stole this money from someone, then it is not permissible to eat it. If you know that your father stole this sheep and slaughtered it, then do not eat and do not accept his invitation. But if it is haram because of the way in which it was acquired, such as if he deals with riba or cheats and so on, then eat, and the sin is on him. 

The evidence for that is that the Prophet (blessings and peace of Allah be upon him and his family) accepted gifts and food from the Jews, who are known deal in riba and consume haram. A Jewish woman gave him a poisoned sheep in Khaybar so that he would die, but Allah protected him against that until an appointed time. And a Jewish man invited him to eat barley bread and fat, and he accepted his invitation and ate. And he bought food for his family from a Jew, and he and his family ate. So let him eat and the sin is on his father. End quote from Liqa’ al-Baab al-Maftooh (13/188). 

Based on that, there is nothing wrong with your accepting this money that has come to you from your relative and benefiting from it. 

If you want to give it in charity to your husband who is hard up, he is entitled to charity if he is in debt and hard up, and it is permissible for him to accept your charity, whether the charity is from this money or otherwise. 

Zaynab, the wife of ‘Abd-Allah ibn Mas’ood, said to the Prophet (blessings and peace of Allah upon him): “O Prophet of Allah, today you enjoined charity, and I have jewellery that I want to give in charity, but Ibn Mas’ood claimed that he and his children are more deserving that I should give it in charity to them. The Prophet (blessings and peace of Allah be upon him) said: “Ibn Mas’ood is right: your husband and your son are more deserving that you should give it in charity to them.” 

Narrated by al-Bukhaari (1462) and Muslim (1000). 

Secondly: 

The owner of the haram wealth has to repent to Allah and get rid of the haram wealth that he has left, by spending it on charitable causes, or giving it to the poor and needy, debtors and the like, with the intention of getting rid of it not of giving charity, because Allah is Good and does not accept anything but that which is good. 

Based on that, if your relative gets rid of this money by giving it to your husband to pay off his debts with it, then he will have done good and your husband can accept it. If he gives it without the intention of getting rid of it and he gives you the money and you give it to your husband, there is nothing wrong with that, as stated above, because you have taken it in a permissible manner which is as a gift, and the sin is only on the one who acquired it (unlawfully). 

Thirdly: 

It is permissible to accept the gift of a kaafir, so as to soften his heart towards Islam or to honour him as a relative, neighbour and the like. The Prophet (blessings and peace of Allah be upon him) accepted the gift of al-Muqawqas, and the sheep given by the Jewish woman. For more information on that, please see the answer to question number 85108. 

And Allah knows best.