Well, I'm afraid that this will not work out at all. It is one of those issues where there is politically motivated will (demographic change, make voters happy etc.) but no one in politics actually bothered to do something effective.
It is hard to say. It really depends on where you are. We had a very hard time finding something and in the end we found a tagesmutter at the other side of town. But some of my co-workers were able to choose between public daycare, private, and a tagesmutter. I live in a neighbourhood which has the highest birth rate in Germany, so I guess our problems weren't that surprising.
So, they made this promise without really providing the funds or means to actually create those daycare slots. All the while pretending that everything is just fine.
Not to mention the reward they have introduced to parents who decide to take care of their children at home instead of sending them to day care (this has caused some stir up this year because it is quite clearly an incentive for mothers to stay at home and will be most attractive to those who are unemployed anyway - and will give them another reason to not start looking for a job. Thus contributing even more to cementing the structures of an increasing number of people who have never worked in their life).
In my town new daycares pop up all over the place. It is not enough, that is true. But I can see their effort. I am fortunate to live in an Eastern German town where the situation is not so bad, compared to places like Cologne or North-Rhine Westphalia in general. (Or Munich, as mentioned in the article.)
And I am not so sure about the unemployment thing - that assumes that every mother who is currently unemployed doesn't want to work in their future and it perpetuates the myth of unemployed people being lazy. I know several single women who are unemployed because they are single moms. As you probably know, it is very hard for single moms in Germany. They get zero support and hardly have the chance to work full time. Many of them need the support of their families to work, because they cannot find daycare. (I know the law changes this, but here in Saxony you wouldn't get daycare if you were unemployed. We always had to hand in forms signed by our employers.) If it was me, I'd rather take a job and daycare than those lousy 150 euros each month.
I agree with you that the whole "reward" thing is ridiculous, for so many reasons. Example: If we look at the situation right now, it is a taboo to send your kids to daycare when they are under the age of one. Daycare for these young children is almost nonexistent. The state cannot and won't provide much daycare for these kids. So they give you a paid parental leave and job security instead. That could be seen as a "reward" as well. But most parents don't really have a choice. Someone has to stay home with the kid because it can be very hard to find daycare for a six month old kid. But staying at home with a six month old is seen as perfectly normal, whereas if you want to stay home with your three year old, most people look at you weird. That seems very strange to me.
I think paying parents money to look after their kids is a good idea. It's a job, too. The thing is, in my opinion, that our government wants us to believe that we have a choice when we really don't have one. Some parents would love to stay at home, but they need the income. For me it was clear I didn't want to be a stay at home mom and I am very glad for daycare. (and I think my daughter is, too.) Those 150€ won't really give you a choice and therefore it's ridiculous and insulting.
And one can figure that a large number of parents will not do anything against this farce because they'd have to sue to get that daycare slot and who these days has the time, energy and means to do just that?
It probably depends on your situation. If you have been looking for daycare for two years, your paid maternity leave ran out and everyone always told you that it's not their fault and their responsibility that they couldn't provide a place for your kid, then sueing suddenly doesn't sound like such a bad idea anymore.
Anyway, in one year our daughter is changing from the current daycare/nursery/tagesmutter to a kindergarten like most three year olds in Germany. Our city just started switching to a system that includes every provider, even the private ones, who have to tell the city administration about the number of their places, etc. They want to make it easier for parents to find a spot for their kids and not make them run about town for months. But right now it's chaotic as hell. Nobody knows what they are doing and private providers try to ignore the new system. I am pretty sure we won't find anything in our area again because kindergartens and daycares always take siblings first.(Which is understandable.) And those siblings take up pretty much all the places.
I still think that in theory this new law is awesome. (Western)Germany has a long tradition of bashing daycare and guilting mothers into staying at home. This law might change this point of view for some people.