My submission for your review and consideration. As requested this is ideal for single color print as well as Tee. The most economical Tee print size is 12" x 12" or 10" x 10" on the front and or back. I've taken this into consideration in designing this logo to maximize the print area.
About the design they layout incorporates a feeling of fun, and importance with out being overly corporate and with the 3 stylized children it is an easily identifiable mark so that people will instantly know it's "Always Beleive".
I've given this much thought especially the unicorn aspect. I am also an amateur astronomer and I knew there was a constellation for the unicorn called "Monoceros" it near the constellation Orion (my fav) and Canis Major (Dog). this is the perfect logo it serves as a beacon on a clear night and all one has to do is look up find Orion it easy then Monoceros is to the left ...When people ask about the logo you can say look to the stars and believe.
Here is link to the layout. I had to resize stars in the design to visually bring it all together but they do align. there are also several minor variations in the actual lines of the constellation this layout I this on e the best for this design
I've also added the constellation name but we can remove, I thought it might be a nice touch to pique interest