If the release button will not push in then you could have ice or frost underneath the bucket that is preventing the catch from releasing the bucket from the mounts on the door. The first parts image below shows the parts of the ice bucket. The release button (Key 19) is attached to the latch assembly (Key 20). When the button is pushed in it releases the latch assembly from the mounting posts sticking up on the base of the door that are shown in the second image. You may be able to defrost this area with a hot air gun or hair dryer on a low setting. Once you are able to free up the latch so that it will release from the posts you will then be able to remove the bucket.
If the assembly is broken, you can order parts from the
website. Order and replace the broken parts to fix the ice bucket.
If you need more help, resubmit your question with additional details.