Hmmm...
A couple things here. How long is the story (word count-wise)? Are we talking novel length or flash fiction? Because if you are asking a professional editor to read it again, and it's long, they may want extra payment.
Stories are very personal, and one person does not hold the monopoly on opinion, what some one feels is extraneous, may be important to others. Personally, I like stories that stick to the point. My favorite books are usually short (Vonnegut, Salinger, ect.). I find King too long-winded, and always want him just to get on with it. On the other hand, even King edits his stuff way down before he sends it to his editor.
Here's my opinion. Just say, 'hey, don't you think that this part is important for the subplot?' That's not insulting, and besides, professionals should have a bit of thick skin. Additionally, I'd give the story to a couple more people. They need not be professionals, but you need people who have never read it before. If they don't get the subplots, then you have a problem with the story and may want to change it a bit to clarify your themes. If everyone else understands the subplot and theme, then the editor missed something.
But, in the end, remember: You are the author. You decide what goes in the story.
Which brings me to my next point, did you know that we have a crit group here? I put a story in last month and got some great advice on it before I submitted. It's a bit slow right now on account of the summer, but we're still kicking and always looking for new members. It's fairly easy to join, all you have to do is ask.