I have some of the abilities that you speak of and that may be a result of some of the other illnesses that I suffer from alongside this on or it may be something else.
As far as having an inner child vs a child alter I think that it may be possible that if you have a happy or innocent type child alter that they very well could be very similar to your inner child. I see my inner child pretty much the way I see my original self alter who existed before trauma occurred but, feeling that way doesn't make me correct about that. It's just how I feel about it or what I think of it.
As for being able to suppress some personalities, I, the host personality have this ability because I am the highest authority in the mind and the others are there to serve me save for a particularly bad one who I have clashed with some in the past.
That particular alter has gotten out of hand before and when I considered him a threat to the system I (in a sense) incarcerated or banished him for a while. I have had to do this to him twice in the past and now we have an understanding although he is still my enemy and vice versa but, we can meet in the mind and be civil toward one another and even agree on some things now and cooperate with each other when it's needed. Some personalities can even go into a state of dormancy if they aren't really an important part of the system or you simply ignore them. I have introjects that I have placed on the back burner before and eventually stopped thinking of them so much and as a result they seemed to have faded away but, are now awake again due to recent, heavy stress. In fact I had one of them on lockdown and refused to let him out for fear that he could get me into trouble but, that problem has been solved as he is now under the control of another introject whom I trust fully to keep him in line. So the answer to this is "Yes" that some people who suffer with DID do have a certain amount of control to a degree even though it is considered to be very rare according to my pdoc.
If you want to discuss it further or have anymore questions just message me and I or one of my other alters will help you out or summon me to help you out.

EDIT: I forgot to add the part about letting child alters out. Though I/We have a lot of control in our system we are still subject to some triggers like for example at Christmas time or Thankgiving, my happy child alter sometimes surfaces or merges with me temporarily because he feels safe to but, the rest of the time I and my other alters keep him deep within and guard him to protect him. If anyone from the outside ever frightens him or hurts his feelings, we avoid that person in the future and perceive them as a threat to us.
I hope this helps you to know more about the things you were asking about.