Well Marco you have found a dilemma that we segmenters deal with all the time and it is challenging. I can speak for myself because I do alot of segmenting with various materials. When working with metals and acrylics the material has no open grain to it where adhesives can seep into and attach like wood fibers. So this is why it is challenging and we rely on a very thin adhesive layer to keep things together. Then when drilling we put pressure on this joint and depending the complexity of this joint it can snap off easily.
Now with that said there are tricks that are used to this day.In fact there is a thread going on right now that talks to this very problem so to show you it is an ongoing problem. Here is the link to that thread.
https://www.penturners.org/threads/trying-the-make-brick-pattern.168814/
Now some quick suggestions that may help and if you do not understand just ask questions. There is a couple methods to make a segmented blank. One is called build on tube and the other is basically called build and then drill. what this means is if you are doing basic segmenting where you are stacking segments on top of each other such as rings then you can cut these pieces and drill them before you stack them. Takes the drilling pressure off the joints. But if you are making complicated designs such as chevrons or scallops and things of this nature you need to build the blank before drilling to keep things lined up. This one is the challenging method. I always prefer epoxy glue. My go to glue is System3 T88 epoxy. It has a long open time and requires at least 24 hours to cure. But it is the strongest adhesive I have found.
Next there is the trick of reinforcing the blank before you put in chuck to drill it. This can be done various ways and in that thread I linked there are several examples shown. But the use of gauze wrapped around the blank with thin CA drizzled within to adhere to blank and give it outside strength. Then there is the method of adding popsicle sticks or other thin woods to build a box around it and gluing it to the blank to again reinforce the sides. Then there was the suggestion of using heat shrink material. But you get the idea. Some people can get away with just flooding the blank with CA to give it strength. Again depends on nature of blank.
Now the act of drilling. Need to use either a drill press that is accurate and no runout and vibration. The blank needs to be held secure. That is why many people drill on the lathe and it makes for a more exacting drilling operation if set p right. Then many people including me like to use the step drill method. That is start with smaller diam bits and build up to one that works with tube. Onec the hole for tube is drilled then the use of epoxy to glue tubes in will add strength to the blank from within if a good layer of glue is used. But again when turning outside forces are applied and thus sharp tools and very light cuts are needed at all times. Again you can reinforce with above methods of CA or gauze if you find a need to. I never had to do this.
One thing I forgot to mention when building the blank it is always a good idea to build it much larger than needed. I always build them at least 1" square and try to keep square till I start turning. Makes it easier to do segments and easier to clamp. Plus it gives added support to the entire blank when drilling. Also when drilling and when turning, as with any blank heat is your enemy. Keep drill bits cool by drilling slow with low RPM and backing out often to clear swarf and also when turning. light cuts wins the race. Good luck.
The more blanks you make the more tips you will pick up and develop on your own because hands on is the best teacher of all. Good luck and lets see what you got. You can check my photo album out if you want to see examples of what I do. Happy Turning.