"Will you see your children next Sunday?"
I think you still need a 你 at the beginning/right after the time, but you are correct. I think this reads as "Will you see children next Sunday?" 下个星期天你会不会见你（的？）孩子？
Also -- I used 星期日 and it flagged it as incorrect. It only takes 星期天。 Not sure if 日 is less used, but I was taught both are OK.
I am a native speaker of the Chinese language and my answer was "你下星期天会不会见孩子？", which sounds perfectly fine to me and yet is not an acceptable answer. The only difference between my answer and the model answer is the missing "个" in mine, which just serves as a classifier indicating the number of the object we are talking about. In this case, I don't think the "个" is necessary as we are not counting the number of Sundays here. Any input on this?