Fallacy?

1. There is no reason to love someone who doesn't love you back.

2. Mother loves her children but children doesn't love her.

3. Therefore mother shouldn't love their children

No fallacy. Of course, premise 1 is debatable.

1. There is no reason to love someone who doesn’t love you back:  There is no evidence to back this up, and it is likely a matter of opinion. However, even when assuming it’s true, the argument still falls apart
2. Mother loves her children but her children don’t love her: This is not true in every situation, but it may be true in some. Let’s assume this question refers to those situations
3. Therefore mother shouldn’t love their children:   This is incorrect, because point one states “there is no reason to” and not “it is bad to” and it does not state (or prove) loving somebody who doesn’t love you back is bad, it simply says it isn’t good. Therefore, a this conclusion conflates  ”not good” and “bad”

Aside from what others have mentioned, we have elements of the ambiguity fallacy from implicitly redefining terms leading to a non sequitur wherein we jump from having no reason for doing something to being advised against it.

If we accept the premises as true, P1 talks about there being no reason to love someone in a given situation and P2 describes the situation occurring.  The logical conclusion from these two premises would be that the mother has no reason to love her children ... not that she shouldn't.

1. There is no reason to love someone who doesn't love you back.

This is an opinion and not an error in deceptive reasoning. Moreover, one might argue that the claim asserts itself from a state of ignorance because it seems woefully unaware of the volumes of music, literature,  philosophy, religion, and transactional psychology that argue otherwise. Ultimately and individually one might dismiss those reasons but to claim they don't exist is a false premise. 

2. Mother loves her children but children doesn't (sic) love her. This has been proven true in the annals of mental disorders (sociopathology), matricide, and domestic abuse, etc. It's much too complex and subjective of an issue to generalize. One might comfortably assert:

Most mothers love their children, but some children do not share that emotion

And not be in error.

3. Therefore mother shouldn't love their children. 

This is clearly a hasty generalization.