It depends on what exactly you are going to do in the family business. If you are just joining the business as another employee but are not going to be in charge or your father still holds on to his spot as the head of the company then you wouldn't say "take over" the family business but would say "going into the family business" or just "I am joining my family's/father's business". However, if you are going to replace your father as head of the company or are going to be in charge so your father can leave the business then you say you are "taking over the family business". I understand why it might sound a little hostile but in this case it just means that you are "taking over" the responsibilities of the business from your father.
Also, a note that I wanted to point out was that "going into the family business" can be used in another way. As an example, if your father was an attorney/lawyer and you decided that you were going to be an attorney/lawyer, you could say that you were "going into the family business" even though you were not going to be working with your father or be part of his business because you were going to be in the same occupation as him. People usually use this phrase in this way when people in their family have been in the same occupation for generations so to fit in the example I gave it would be you were an attorney, your father was an attorney, your uncle was an attorney, your grandfather was an attorney, your great-grandfather was an attorney, etc. I hope this information helps:)