1. As far as the properties left behind by your deceased father, it devolves equally on all his legal heirs, i.e., your mother, you and your siblings.
Your mother cannot become the successor in interest to succeed to the entire estates left behind by your father.
Since the said properties devolve equally on all the three, you may enter into a formal partition among yourselves to divide the said properties among yourselves on the basis of amicably agreed conditions. The partition deed may be drawn and get it registered..
You can divide the properties into three schedule of properties with one schedule allotted to each.
2. The property purchase jointly by you and your brother belongs only to two of you and your mother or anyone do not have any rights in it, you can divide the property by a mutually agreed partition deed and the so drawn partition may be recorded in a registered deed.
3. The property transferred by your grandmother to both of you becomes your absolute property. Please note that the grandmother's property is not ancestral proeprty, hence the property transferred to both your names by a registered gift deed becomes your own and absolute property hence neither your mother nor any other person can claim any share in it as a right.
You can divide the said property also by a mutually agreed partition and the same may be drawn by a registered partition deed into two schedule of property.
4. After having done with all the above three registered deeds, you and your brother can decide about exchanging each other's share in the said properties to each other and draw an exchange deed, get it registered.
After this process is completed yo may get the revenue records transferred to your respective names accordinlgy.
5. The proposed registered release deeds will actually confuse and if not done properly then the title will be defective in all the properties, therefore you can better do it patiently by deciding the proper mode of transfer instead of suffering the legal hassles at a later stage.
You can discuss with an experienced lawyer before taking any further concrete steps in this regard.