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, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The deceased’s mother gets one sixth of the estate as a fixed share because the deceased has children. Allaah, The Exalted, says (what means): {And for one's parents, to each one of them is a sixth of his estate if he left children.} [Quran 4:11]
The residue of the estate should be divided among the deceased’s son and two daughters by Ta‘seeb (i.e. by virtue of having a paternal relation with the deceased and not having an allotted share, so they get what is left after the allotted shares have been distributed); the male gets double the share of the female. Allaah, The Exalted, says (what means): {Allaah instructs you concerning your children: for the male, what is equal to the share of two females.} [Quran 4:11]
Hence, the estate should be divided into twenty-four shares; the mother gets one sixth of them (4 shares), the son gets 10 shares and each daughter gets 5 shares.
As for your remark “the deceased persuaded the relatives that all her three children manage her property without sharing”, then if you mean that the deceased has convinced her relatives that only her three children would inherit her (disowning the other heirs), this is considered a bequest made to an heir; in fact, this is impermissible as per the Sharee‘ah and it cannot be executed without the consent of all other heirs. The Prophet, sallallaahu ‘alayhi wa sallam, said: “Verily, Allaah has given every rightful person his due right; no bequest should be made to an heir.” [Abu Daawood] Moreover, Ibn ‘Abbaas reported that the Prophet, sallallaahu ‘alayhi wa sallam, said: “Verily, Allaah has given every rightful person his due right; a bequest made to an heir is not valid unless the rest of the heirs agree to that.” [Ad-Daaraqutni]
Therefore, if the deceased’s mother gave her consent to that bequest and was willing to give up her share (one-sixth of the estate), then the bequest may be implemented (and the deceased's estate should be given to her children only); otherwise, she is entitled to her full share (one-sixth) and the bequest should simply be disregarded.
Allaah Knows best.