Parents NEED to understand the difference in age. Don't YOU hate it when you have to stop watching a movie you are interested in mid-way and do something you don't want to. Well a child has a harder time coping. Imagine your mother walks in on you fucking your girlfriend, and says in a pleasant voice (she ain't being a bitch) "honey, please get out of her and wash the dishes". Imagine the response you will have. Now imagine the request "honey, I know I'm heavily intruding but you haven't done the dishes in 3 days and I am hungry, so finish up in 15 minutes and wash the damn dishes!" I assure you the second scenario will make YOU feel responsible for the fact that this shit happened, maybe even embarrassed. But the message is VERY different. There was no painless way to get into the situation but it was as painless as possible given the circumstances and the blame now lies in the appropriate party.
You need to alert the child that "homework is coming" give em a few minutes to cope, make sure they understand they have a few minutes and let that brain work at the coping, it just takes time. Be consistent with it. Also important to let the child know why it's their fault they have to stop, if the child did the homework first the child would have the ability to watch the movie without interruption. (make sure to not go back on your word, because that will not help later on). Now if the movie is on disk, let the child know you can pause and resume later, if not, hell 5 bucks to download the movie and let your kid watch it is worth it.
With children every potential conflict can be turned into a learning experience one way or another. The problem is the going up to a child "turn of the tv and do homework". To a child that might be too sudden and too intense to immediately cope with.
I am 26 years old and already me and my wife noticed these little things. Most the conflicts with my 3.5year old is avoided. AND she does what we want her to do. Sometimes we turn chores into a game, sometimes we turn something she dreads into something "fun" because we join her. Also PICK YOUR CONFLICTS. Believe it or not, the child will want to do things differently than you do. Sometimes the way the kid wants to do it is alright, so let them have their way. The child NEEDS to feel some control over their life, give them inconsequential choices "red or blue shirt" fine it does not match, who cares.
You will have to dedicate yourself to the kids, but thats what parenting is about.