Welcome to the forum.
Interesting question. I have been thinking about ways to minimize the projected sound of my melodicas so that the audience in a small venue hears more of the sound coming out of my amp than the acoustic sound of the melodica. I want to do this because I process the sound through effects pedals and want the audience to hear–ideally–just the processed sound.
My ideas include: (1) partially surrounding myself with sound-adsorbing tiles or panels including a sound adsorbing rug, (2) using a clear plexiglass drum shield, (3) attaching some sound absorbing materials to my melodica, (4) using a microphone isolation shield, and (5) trying to get my amplified sound as loud as possible without feedback, so I can play softly.
The last two ideas will not help you as they are intended for performance. I have not tried to implement the first three ideas yet as I am still thinking about which direction could be best and least intrusive on a stage.
I can tell you, that if you buy a melodica with the sound holes on the back (there are only a couple of models like this in the world), you can hold the back of the melodica tightly against your chest, effectively muting it. It is a funny position to play in, but I do it fairly often. If you play softly in this position, the melodica volume is reduced substantially. Maybe if you had one of the melodicas, you could put tape or other materials over the holes.
Note: Many melodicas have holes on the back for ventilation and maybe some sound tuning, but only a few models actually direct all the sound out of the back side of the instrument. On most melodicas, the sound is projected out through the keybed.
So, I think for now, the best advice I have is to go to the room farthest from the children, shut all the doors in between, and play softly. If you develop a good technique for muting your melodica, let us know.