If you had established the business before you told your relative about it, then yes it would be haram and that you should have told him about the business established and the income made from it and ask for forgiveness or return it to him. For stolen money used and income coming out from it is all haram.

 

But as I understood from your case, you kept the money as it was and you went and cleared your fault with him, returned some and kept some (with your relative knowledge and approval), then that money became more like a gift from him to you and it is cleared being halal insha Allah.

 

Based on that, the investment in it and making money as profit from it is Halal. And it should be fine.

 

Now, I suggest, for the wellbeing of your conscious that when you save enough money to even go back and offer him the 2000 dollars one more time and that if he refuses to take them as he forgave you before and had given you the amount with clean heart, ask him to donate it for the poor and needy.