Rip said (and some others said much the same, not picking on your post Rip)How can I expect my toddler to learn to answer me and/or do what I ask when I ask, if I don't do the same for him? There are far too many double standards IMO.
IMO there are two parts that need addressing to answer that fully.
The first part being that you teach them that you are the parent and they are the child. It is NOT an equal relationship and it needs to start when they are young or else how do you expect them to respect you and do as they are told when they are older? It may be considered 'old fashioned' but they answer you and do as they are told because YOU are the parent.
The second part being Interrupting conversation Once again you are teaching them life/social skills - 'you don't speak over someone else, you wait your turn'. It's something MOST adults do automatically, but something we all had to learn. You can start teaching this from a very young age.
When they are very small (up to around 15 months) smiling at them & immediately picking them up and sitting them on your lap while someone finishes their sentence then talking to them is my way. From around 15 months (depending on the child and their grasp of language) immediately saying wait a minute (while holding their hand or picking them up) is starting to teach them social skills, from around 20 months they can understand (depending once again on their comprehension level), a bit, to wait until someone has finished actually speaking (THAT sentence not a conversation), and you build on that - that way, by the time they are around 3 they understand you need to wait until someone else has finished speaking (several sentences, but not a FULL conversation). However, I fully expect to have to continually remind a 3 year old of this, but for them to have it sorted by the time they are around 4 at which point they get told quite firmly to mind their manners!
You don't need to 'bark' or send them away, you can hold their hand or have some form of contact with them and you can show some adult commonsense about what to say with small ears listening and for how long they are able to wait patiently. I am meaning for a minute or so - not a long time.
IMO anyone who completely indulges the childs every utterance teaches them that they are the centre of the entire universe and makes them very difficult children who then have to learn the lessons that could have been taught much earier and easier in life before they have developed the bad habit of speaking over people.
Once again IMO completely child centric parenting is, as a society, getting us into a lot of bother. They grow up believing they can do as they please and then when they do so as young teenagers (drink, fight, happy slap - whatever), parents are suprised?!
We need to parent children, not indulge them.