I have installed CoreELEC to emmc and i noticed the boot order now is that it first boots emmc, no matter if there is an sd-card inserted or not.
Is there a way to change this, so the box first tries to boot from sd-card, if any is inserted?
No it’s not changed. Try another media or USB. emmc is always last option.
I just noticed that i forgot to mention an important part. My question above was not about the recovery boot with the toothpick, then it really boots the SD-Card first.
I look for a solution that the box boots from the SD-Card first without using the toothpick. Just a normal boot and then it boot always emmc first here 
Then your unknown vendor did change the order on your unknown device bootloader.
No way to fix it.