This is about boundaries and being honest. Arr you sure she expects to go?only talk about her going if she asks to go. Kindly tell her that the older sisters want to go by themselves. Then sympathize. Listen to her as she feels hurt or angry. If she's willing to have a discussion, talk about the reason. Leave your description of her personality out of it.
You have reasonable reasons to not take her. Play up the age and differences in life experiences, the lack of things in common, the need for you all to have a break from the routine of motherhood. Be kind, don't waver. Be sympathetic. Be careful to not get involved in her reasons to go. Just repeat that this trip is for the older sisters.
If your sister is not getting help for depression encourage her and her mother to get professional help. Have this discussion later. Her not going is not because she's depressed.
Making your sister happy is not your responsibility. Taking her on the cruise is not going to make her depression lessen. She will feel the difference in her life and yours. The best way to help her is to not take her. I also suggest that you will resent her if she goes. This would make your relationship with her difficult.
Talk about the cruise of the older sisters. Assume she's not wanting to go. Keep conversations light. Only have a discussion if she brings it up.
The cruise is expensive and a big deal. Doing things with her in or on other trips with the family is very different than a cruise.
Geez! I urge you to take care of yourselves!!!! If she goes, you will not be taking the cruise you want. It really is not our responsibility to not hurt feelings. Each of us, including your sister, is responsible for our own feelings. Why do you think you should sacrifice your happiness so you don't hurt her feelings. Everyone experiences hurt feelings. That's OK. She will deal with her feelings.
Would you let your 6 yo ride the bicycle in the street because his 12 yo sibling rides in the street? It's a fact of life that older children can do things the younger children can. She's 17. You're 30. There is a wide difference in age and experiences. You have your life. She has hers.
Has the family always protected her from experiencing hurt feelings? Does the family, frequently, do for her, allow her to participate just because she wants that. If so, she hasn't learned how to deal with having hurt feelings.
I understand not wanting to hurt her feelings. I've been there. I was depressed. I allowed my daughter to do things I really didn't want her to do so that I could have peace.
My philosophy was to always meet the parents and the children before my daughter could be at their house or spend time with them. She asked to go to a "friends" house and I said yes. She wss 12. She was raped.
I believe it's my responsibility to keep her safe. I failed! It's also my responsibility to take care of myself so that I will have the emotional stamina to be kind and firm when I believe it's best for both of us.
Your situation is different. It has similarity to yours, however. You don't want to take her because she is young and will cause your trip to be totally different than what you need and what you planned. You're sacrificing your happiness so she won't get her feelings hurt. If she's on the cruise, none of you, including her, will be happy. There will be tension. I suggest by taking her all of you lose. There should be a boundary between the older sisters and the young sister, based on the wide age difference. This is to be an adult cruise. 17 yo don't get to do the same things as the over 30 sisters. That is life!
Perhaps your sister, in part, is depressed because she lacks reasonable and clear boundaries. She doesn't know where she fits. People give in to her and she knows in some level that what she wants is inappropriate. A teen needs clear boundaries while she learns about herself and the world.
I hope you give some thought to this. I suggest you learn about co-dependancy. It's a situation in which we sacrifice ourselves to make others happy. A codependent's happiness depends on the happiness of someone else. What you wrote is that you're willing to sacrifice your own happiness so that sister won't have hurt feelings. Would you take your children on a romantic weekend with you spouse? Of course not. Your situation with your young sister is similar. Why would you take teen on your adult cruise?
Adults get to do different things than teens.