How does she go about this given the facts above?
One of the biggest challenges she’s going to face is having her teaching credentials recognized in Germany; she’ll need to show proof of level B2 German skills and might have to do additional training here. If she wants to work in Baden-Württemberg, she should get in touch with the Regierungspräsidium in Stuttgart. Have a look here and here.
What is the best way of securing the erzieher/in jobs? Does she reach out to municipalities directly?
She could take a look at the Jobbörse from the Agentur für Arbeit. If she knows where she wants to be, she could also get in touch with towns--the village where I live posts job ads on its website, for example. Schools that offer the Erzieherausbildung might also have job listings from kindergartens in the area.
Would municipality run centres consider her given that she is miles away and a non resident?
If she doesn’t live here and doesn’t speak German well, then no, they’re not going to give her preference over local candidates.
Is the need for erzieher/in serious to the extend of recruiting overseas candidate?
The need is serious, but most places aren’t recruiting overseas, as far as I know, especially given that it’s quite difficult to get foreign qualifications in the field recognized. They're mostly focused on expanding teacher training opportunities within Germany and convincing people to do the Ausbildung.
You didn’t mention how old your daughter is. If she’s young enough, she might be eligible to do a Freiwilliges Soziales Jahr and work in a German kindergarten for 6 months to a year, which would give her the chance to work on her German skills (most FSJ positions require B1 or so), and then she’d already be in the area when applying to jobs. She might also be able to find work at a private kindergarten as a "language assistant"/native speaker. In any case, she’d do well to look at the Anerkennung in Deutschland site above first and find out what she would have to do to get her qualifications recognized. I’d be happy to talk to her if she has questions--I’m from a non-EU country and am doing the Erzieherausbildung here in Germany, but I have friends who have gone through the process of getting their qualifications recognized.