I would like to join a llm-program, but I need a daycare faciliy for my child. Is there someone, who has good experience in this respect?

Have you considered distance learning as a viable route to maintain family commitments whilst also studying for your LL.M. Not only could this potentially allow you to widen your choices of institutions (there are many from the UK, who offer top-class LL.Ms via distance learning) - you could also save money on travel and/or relocation as well as day-care costs. Not to mention the extra time you'd have with your child! It may not be the perfect solution, but you should certainly consider distance learning.

I hope this is of some help!