Do i have to invite his adopted daughter

If he wants his daughter there, she should be invited. If he doesn't she shouldn't. You are sharing a lot of backstory but what does he actually want? It should be a black and white answer.

It sounds like he wants his cake and to eat it too. He doesn't want to invite the adopted daughter, but also doesn't want the fall out from the decision. Unfortunately, that may not be possible. If she's going to get upset and/or cause drama about it, then that's what she is going to do. I don't think lying to her (falsely claiming it was a last minute elopement) is going to cut down on a reaction/drama though. She will undoubtedly find out when her brother is not only invited to, but also a part of, the wedding. If your fiancé doesn't want her there, he needs to stand firm in that decision and handle any backlash that may happen because of it. It's ok to not want to invite toxic people to your wedding!

If she doesn't live with you, I'd ask the people you're inviting to your intimate wedding to respectfully please keep your wedding to themselves. Let them know you're very excited & nervous about the wedding & planning & have decided to only invite your very nearest & dearest & that you'd like to make an official announcement after the event.
This way it conveys the importance of the guests keeping the information to themselves & makes them feel really special that they get to come to a very special & exclusive event.
After the festivities have concluded, you could always take his daughter out to dinner to share the news. I'd say invite her over but if she has proven problematic in the past, a public place may be best to keep everyone feeling neutral. Let her know you're very excited to share the news & because you're both private people, you had a very small wedding & just wanted to share the news. I'd follow with directing the conversation onto her & ask how she's been, how's work, what has she been up to, etc.