"对小孩等管教不严" can be translated into English as "being lax in disciplining children (and others, if applicable)" or more naturally as "not being strict enough in disciplining children (and possibly others)".
Here are some example sentences to illustrate its usage:
1、 Some parents are being lax in disciplining their children, which may lead to behavioral problems later on.
（有些父母对小孩管教不严，这可能会导致孩子日后出现行为问题。）
2、 We should not be too lenient or not strict enough in disciplining children; a balanced approach is necessary.
（我们对小孩的管教不能太宽松或不够严格，需要采取一种平衡的方法。）
In these sentences, "being lax in disciplining" or "not being strict enough in disciplining" conveys the idea of not exercising sufficient control or authority over children, which aligns with the Chinese expression "对小孩等管教不严".