What a dilemma. I faced just this situation a few years ago when a mother came to me with three children. I immediately wanted to teach the older daughter and the younger daughter, but didn't want to teach the boy in the middle. There were lots of reasons why I wanted to teach the oldest and the youngest—they were interesting children, completely ready for lessons and I immediately liked them. They'd had some "lessons" with another teacher, but I could tell right away that they would be successful piano students.
The boy was completely different. He was definitely hovering at the edge of the autism spectrum and had great difficulty controlling himself. That wasn't what actually mattered in making this decision. Yes, he had some physical challenges that would make piano playing difficult for him. But even more important was the fact that he was fiercely competitive with both of his sisters. Even in the interview, he compared himself to them constantly. Trying to teach the three of them would have set him up for nothing but frustration.
Years ago I might have thought the only options were to take all of them or none of them. I've gotten wiser in my dotage.
Here was my solution:
I took the mother out for coffee. Sometimes it's easier to have difficult conversations in person. You can make eye contact and use non-verbal cues to convey your sincerity and warmth. Email can be particularly treacherous in situations like this, especially if you're just getting to know someone.
We met in a Starbucks to discuss the situation. I explained why I thought that having all three kids playing the same instrument was, in this case, not advised. I clarified exactly why I thought that playing the piano, specifically, would be more challenging for him than it would be for his sisters.
She agreed with me that he was too competitive to tolerate watching his sisters shoot ahead as he struggled. He needed something that, by definition, would make him special and make comparisons more difficult. I felt that it would be better if her son played a completely different instrument and suggested the guitar. (The guitar is easier to play, especially at the beginning, and almost impossible to compare to the piano.) I was completely honest with her about my assessment of the situation. And though I was kind and understanding, having raised a difficult boy myself, I didn't offer to take on her son as my student. I took the girls and, as I'd predicted, they did quite well.
Here's the thing: if you can see heading into a situation that it won't be successful, follow your instincts.
Any healthy parent would always prefer your honest opinion as long as you are kind, gracious, and offer another solution that will work better. You'll be doing no one a favor if you teach a child that you think isn't a good fit, even if the siblings are studying with you. It's far better to follow your heart and speak the truth kindly.