What could be the reasons to be rejected as a Doctoral Candidate in Germany?
Without knowing more about your specific case, here are some potential reasons (in no particular order) why you might not be getting the job(s) you are applying to:


your profile/prior experience is not as relevant as you think it is for the position
they already have somebody in mind
they might think, having been in the industry for some years, you will look into doing research as a "9-to-5 job" (for better or worse, in most countries academia is different than industry). I am guessing this is what you refer to, with mentioning kids? I have plenty of colleagues with small children, that alone is not a problem. 
they are concerned you do not fit the rest of the team
they found somebody better than you
they might be concerned about your reasons for switching to academia


Without more information it's impossible to say which one, if any, or which ones apply to your case. Your best bet to ask for feedback when you are given a rejection. It's important, and I cannot stress this enough, to be polite when you do so. The idea is to get meaningful feedback so you can improve your chances for your future applications, and definitely not to get a justification for their decision. They have absolutely no reason to justify their decision to each individual applicant. 

What kind of feedback you get back will ultimately vary, sometimes you get a meaningful message with relevant feedback, other times you will get the boilerplate "we regret to inform you..." and not much more than that. Most often you will get something that is general enough, but with some nuggets of feedback. 

For example, I recently got a rejection from a consultancy company I sent a general application to. I was introduced to them for the first time last year, when they were attending a career fair part of a conference I helped organize. I asked for some feedback, and in between the typical corporate HR BS, there was the indications that they had pivoted away from the areas where my skills would be valuable to them. So my take home message from that is that this company is not relevant for me anymore, even if it may have been last year. And yes, even if the job description fits my CV really well, they are not looking for someone like me. 

I am giving this example only to serve as an example, I am sure your situation will be very different. But the point is, try to read into whatever feedback you might get. 

Lastly, if I were you, I would try and see if there are any possibilities to get some career coach or something like that. It would be good to get some recruiters point of view on your CV.



EDIT: I noticed that I didn't address some of your questions


  Are there some special differences applying for jobs in the industry compared to academia?


Well, yeah... I would guess that academia would put more weight on your prior education, what courses you have done, whether or not you have published anything etc.

Industry, I reckon, cares more about your prior work experience, i.e. what you have done before. 

The core difference is that academic positions are aiming at you developing your skills, learning new things, acquire a critical understanding of complex subjects. Industry positions primary require you to do something, have a contribution in the value chain in whatever the company is selling to its customers. You improving your skills, learning new things etc is a secondary concern. You being critical of your own, others' or even your superiors', work would not fly as well in industry as it does in academia, I would guess. 


  all applications were the same as I would apply for a job in the industry, which was always really easy and successful - max timespan from sending the application over the interview to job offer was about 1-2 weeks


How many jobs have you applied to? Think of it as a sports stat, if your 3-point percentage is 1/1, sure it's 100% but you are hardly league's best 3pt shooter. :) 

In general, I think academic positions are not filled as quickly as industrial counterparts. There are many things that need to be cleared by the dept/faculty/university admissions etc. Also the positions need to be open for a minimum of X working days, depending on the institution. 

TLDR: Stay patient, ask for feedback, keep trying