Children's play equipment and 儿童乐园
儿童乐园 is children's playground, not play equipment.

The general term referring to play equipment is 游乐设施 (uncountable) or 游乐设备(countable). If you are referring to specific equipment, there are specific names for them, such as:


跷跷板 - seesaw
滑梯 - slide
猴架 - monkey bars
沙池/坑 - sandpit


As for the translation of the two sentences, I would go with the following:


  
  我带孩子们到公园玩。大的喜欢踢球，最小的则喜欢使用游乐设施。
  我儿子的学校有两套游乐设备。(Google Translate)
  



To further distinguish both 设施 and 设备, quoting from 汉典:

设施


  为某种需要而建立的机构、系统、组织、建筑等


设备


  指成套的建筑或器材


So, if you are referring to the whole installation, use 设施; if you are referring to individual equipment, use 设备.