This noun phrase ("our loved ones, ...") is grammatically correct. All the plurals are managed properly, and the student used commas correctly for lists of more than two things.
The problem is in the choice of things to list.
There are four things being listed:
The writer of this sentence needed to give more thought to the fact that, in English, loved ones is a group that includes children and often some of your friends. Normally, co-workers are not included in this group.
A diagram showing these relationships might look like this:
So the point is that loved ones and children are redundant, since loved ones includes children. You don't need both.
Get rid of the one that has the smallest affect on what you're trying to say. This is the one with the least impact on your meaning.
If we get rid of loved ones, the diagram looks like this:
You see here that we keep the children, but lose all the various other loved ones that are so important to our lives (parents, brothers, sisters, uncles, aunts, cousins, nephews, nieces, ESL instructors, etc.).
On the other hand, if we keep the loved ones, but get rid of the reference to the children, the diagram looks like this:
You can see that by keeping the loved ones, we also keep the children, as well as all those various other loved ones. This has the smallest impact on what we're trying to say, and this is what we want:
Everyone who is important is included in this list, including our children, who number among our loved ones.
There is a little bit of overlap between loved ones and friends. But it's a small overlap, and it's OK.