I was told that the following does not work:
Employees having children will be granted a day off.
However, this sounds better:
Having children, those employees will be granted a day off.
What is wrong with the first clause?
There is nothing technically wrong with either sentence, as far as I can see.
Subjectively, I prefer the first one, as it is more simple and closer to normal conversational English.
The second example, in my opinion, is a needlessly complex way of avoiding the first version. It would be much better to avoid the problem entirely and say:
Employees with children will be granted a day off.
However! There is a school of thought that discourages the use of present participle with the verb to have when talking about possession.
"I have a car", not "I am having a car". "He has a daughter" not "He is having a daughter".
In standard British or American English this is true. The sentence is completely comprehensible, but would be considered odd in normal conversation. In English spoken by people from the Indian subcontinent, however, I believe it is a common and acceptable regional variant.
But in your sentence, that is not how 'having' is being used. I think (and some better grammarian than me can correct me if I am wrong) that we're dealing with a gerund clause in the first sentence, not a present participle. 'Employees having children' is a gerund clause which acts like a single noun, and is therefore perfectly acceptable in standard English.
Think of it this way:
[Employees having children](subject, noun) will be granted (future passive verb) a day off (noun, object).
When viewed in that way, the first version is a very simple subject > verb > object sentence.
So if your English teacher told you the first sentence is wrong, you should tell them to Google 'gerunds'. ;-)
More information on the use of "the progressive aspect with habitual actions, completed actions, and stative verbs" in the English of the Indian subcontinent can be found here. In this context it would be perfectly normal to say something like "He was having a car".