Yes but what I mean is that "Mother-and-child welfare centre" might be a direct translation (some German news sources are calling it Mutter-Kind Einrichtung, whereas some call it Jugendeinrichtung) but it doesn't really encapsulate what it is because the facility doesn't exist in English and doesn't have a set definition even in German. So some people are picturing a womens' shelter, a medical facility for psychiatric treatment or something as bureaucratic as a benefits office - all sorts you could assume from that description. I'm not really sure TBH exactly what kind of facility this is, I just know that those places can be multi-use and the reports are saying the context and setting for the attack was a meeting relating to custody arrangements for this baby.
And "family-related" is again a direct translation of the wording they tend to use to mean "domestic violence" - it's not a bad translation, it's just that the connotations are very slightly different (IMO)
I would be wary about reports that are leaning heavily on the father's Turkish heritage because racial tensions are high in Germany right now. AfD are keen to push a narrative that all "foreigners" (but especially from middle eastern or adjacent countries) are violent savages who don't follow good Christian German laws, a bit like Reform in the UK. It might be that the father is involved with some kind of criminal organisation, but it might also be speculation.
There is a local newspaper/radio station with an article on their website reporting that the baby was taken to hospital at a few weeks old and the doctor diagnosed shaken baby syndrome, which triggered a whole cascade of things but as I understand, both mother and father were originally suspected of mistreating the baby. Then a "godmother" (I thought a mistranscription of grandmother but it is definitely "Patentante" = Godmother) has come in to challenge this and the parents have had legal advice etc, and so the baby is living with its mother but in this possibly supervised (?) type accommodation. According to that report, social workers and other government (likely local gov, as everything is extremely localised and siloed here) officials had been reporting that the father has been extremely aggressive and obstructive all the way through and the godmother has denied this and claimed it's all lies. Given how he has acted now, I think this is pretty unlikely, but it does sound like her word has been given a lot of weight, which I find strange. Germany is more religious than the UK but I didn't think godparents had legal status - I could be wrong about this though.
There is also some speculation about the woman driving the getaway car, who is about 20 years older than the man (so maybe an assumption, but probably not a girlfriend) and also described as some kind of support worker helping the family, which is strange. I wondered whether she might even be the Godmother who seemed to be very involved, because if she was a professional then it might make sense that her opinion was given more weight than if she was just a friend of the family. And I found it alarming that somebody had previously insisted that reports of the man being aggressive were false when he was clearly an extremely violent and dangerous man, even if he hadn't acted to that extent before.
Shaken Baby Syndrome I read a few months ago is a highly disputed diagnosis and may not even be real. I don't know enough about it to say if that means anything. Medical professionals suspected mistreatment of the baby, which seems the most important information.
What the whole thing makes me think is that it the family situation sounds fairly chaotic and badly managed, and it highlights again an issue which has been recurrent in Germany where the various professionals involved with a child at risk or a family aren't always in contact with each other and so nobody is building up an overall picture of the situation for the child/family.