Translation:They would like to watch a movie tomorrow.
The 想 is before the time marker since it is saying that currently, it is their desire to watch movies tomorrow. The sentence you wrote while not necessarily incorrect implies that the desire to watch movies is happening tomorrow (not necessarily today)
This really makes no sense. The desire to watch the movie is always happening tomorrow no matter the position of the 想, so still don't really get the difference
There are two verbs in this sentence! I'm not sure about the exact rules but "tomorrow" refers to see a movie and it seems to be correctly placed before the verb 看! I usually think like
They want (something) Something = they see a movie tomorrow
If you haven't studied pinyin and Chinese phonetics specifically, you should take the time to do it, here is a good starting point: https://chinese.yabla.com/chinese-pinyin-chart.php
Not really about this section but I'm posting here as it's on my mind now, and hope it might help others. Because 想 can mean: want, miss, suppose, believe, think, wish... I find it helpful to define it (想) as "think about/ of". When you want something, you think about it, when you suppose something, you think about it, when you miss someone/ thing... etc.
They would like to see a movie, not watch a movie, unless they want to watch a movie on television.
Doesn't 想 also mean planning, thinking, considering? so can't I use one of these words in the sentence?
That is very different from the intended meaning. They "would like" does not mean that they would end up seeing the movie. It is their desire. That is why 想 is used to show that.
They are going to see a movie tomorrow = 他們明天會去看電影 / 他们明天會去看电影