All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
First of all, we ask Allaah to reward you for being keen on performing good deeds and for your wish to be kind to your mother and to guide her to the truth.
There is no doubt that being kind to your mother is an obligation upon you and the greatest act of kindness to her is to advise her and explain the truth to her. The Prophet said: "The essence of religion is giving advice." [Muslim] So this advice is more confirmed for your mother.
Therefore, you should be keen on advising her and reminding her about the matters of her religion, especially to observe the Islamic obligations, mainly the prayer. The prayer is the relationship between her and her Lord. If she does not perform the prayer, then she has indeed cut this relationship.
It is for this reason that some scholars are of the view that whoever does not perform the prayer out of laziness is considered a non-Muslim. As regards a person who does not perform the prayer at all and considers that the prayer is not obligatory, then he is a non-Muslim according to the consensus of all the Muslims.
Therefore, you should remind your mother to repent, and encourage her to do so. Also, explain to her that the Mercy and Forgiveness of Allaah are vast.
You should use different ways of calling her to Islam, like letting her listen to some influential lectures on tapes, or by inviting one of your female friends who is wise to perform this task. It is quite likely that a non-related person may have more influence on her than a relative. In addition to this, do not forget to supplicate Allaah as much as possible to guide her. Allaah says (what means): {He whom Allaah guides, he is the rightly guided.}[Quran 18:17]
On the other hand, acts of disobedience have negative effects on the person, so it might be that the depression and instability that your mother is experiencing, are due to the negligence related to her religion. Our advice is that you should advise her, but refrain from thinking about matters of no benefit, like saying that Allaah will not forgive her, and so on. Allaah says to His Prophet (what means): {So remind them (O Muhammad); you are only one who reminds. You are not a dictator over them.}[88:21-22]
Allaah also says to His Prophet (what means): {So destroy not yourself (O Muhammad) in sorrow for them.}[Quran 35:8] So we fear that this thinking would lead you to unpleasant consequences.
Finally, we remind you about the following matters:
Firstly, being kind to your mother is the best way by which you can guide her.
Secondly, the dreams that you have seen should not be taken into account, as they might just be the whispers of your desires or of the devil to cause you grief.
Thirdly, the statement of your mother "The people who fast and pray and observe the Hijab are not all good people" may be correct, i.e. they might mistreat other people, but what should be said to her is that a person who does not obey the commands of Allaah and transgresses His prohibitions is not good at all, and might lose this worldly life and the Hereafter.
Allaah Knows best.