I think it would sound good to make it, "A school that is deeply committed to children's education." Another option would be, "A school committed to excellence in education." Or even just, "Dedicated to excellence in education."

Both versions are ok. But not quite how a professional motto would read. It is a little too long. I personally think you should remove the first word "Establishing" and replace with "committed or dedicated to". Establishing is in present continuous tense you are still establishing. "Committed to / Dedicated to children's education" is all you need. As your motto. Then below on the curriculum or whatever you send/give out/supply to whomever. You can explain further, that education is not only about class work and exams. it's about developing a child's temperament and more.

Committment to education does not mean the same thing as committment to children. "Committment to children" is more broad. An example from current events: If a child tells his teacher that they are transgender, but does not want her parents to know, should the teacher tell the parents? If a school is "committed to children," the most likely answer is "no." If they are committed to education, the answer might be "It depends on whether that will affect the student's ablilty to learn."

You should also find a latin translation. That's what western schools do especially the best schools. From google translate. "Dicata puerorum educatione" But you should check the translation with someone who knows Latin

Both ways sound fine to me, with "children" and with "education". If you wanna make it shorter, I think you could erase the verb and just say "a school that is deeply committed to children", it still sends the same message.