If the Italian authorities granted your mother a residence permit for Italy and you then travelled with her to Germany, it is most likely you would all be returned to Germany. Your mother would have no entitlements to residency or healthcare in Germany. The only case like this in which a person might not be returned is if it could be proven that Italy does not provide adequate living conditions and healthcare. Such a case would be complex and likely go to court; there is no guarantee you would be allowed to stay.
In addition to your mother not having residence rights in Germany, you would also not be entitled to stay more than 90 days of visa-free travel.
If you have permanent residency in Italy (called ‘soggiornante di lungo periodo’), the rules are different and you could apply in Germany for a residence permit to work here. You would have to show a job offer to obtain this permit.
In addition to the residency rights, there would also be questions about custody and visitation rights of your husband. It could have serious consequences if you remove the children from Italy without his consent.
If you have an unaccompanied underage child in Germany, my question would be why he is not living with you in Italy. If he has applied for asylum and not informed the German authorities that he has a parent in Italy, this can have consequences for any possibility of him getting residency in Germany.
However, if you feel unsafe in your current living situation, I advise you to first seek shelter in Italy. There are places of refuge available to women with their children throughout Italy. If you tell us roughly what part of Italy you are in, we can find such an organisation. They can also generally help with legal advice, translating etc. Once you have first found a secure environment for you and your children, you can then look further at what options there may be available for you to come to Germany. What I have written is just a quick first assessment of your situation. You can also contact me and other advisors on the app mbeon. There you also find advisors who speak Arabic and other languages.