The trouble is, you're trying to do too much with this and your hierarchy is wrong. The "alon" mark in itself is okay... and contrary to what other posters have said, it doesn't have to be readable UNLESS you are trying to convey it as a stand alone word mark. For example, Nike swoosh doesn't say Nike, but you see it as Nike because of how they have branded it. With your highly stylized alon type, it comes across more as a symbol than a word mark, so you might have to help it out a bit. Back to the Nike example, when they first came out with it, they added Nike text below it. Now it stands alone. You could go the same route in order to save your mark.
Here's what I would try:
I would treat "alon" as a mark (especially since you've already have it established), but I would add the text alon alongside the mark in a very readable but complementary type face. Next, I would make the "design shop" and "switzerland" more of like a tag line. So, the visual hierarchy would be... alon mark > alon name in type > tag-line. This way, the first thing people see and notice is the mark, then the name that reinforces it and finally the tag-line to say what it is.
You can set up the visual hierarchy with size, position, and contrast. They need to be visually integrated, but read separately. As you have it in your original logo, the Design Shop Switzerland reads first, when that should actually read last (unless it's the primary part of the name). You are adding your mark as an accent and then expecting people to be able to read what it is.
Let me know if you don't understand what I wrote.
