Long term capital tax exemption from sale of joint property

Hello experts, I have a question around long term capital gain from sale of joint property.

I am in process of selling my residential house in City X which is jointly registered between me & my mother. So the questions I have are:

1. Can both me & my mother buy property each in our respective names (seperately) and we both be eligible for exempltion under section 54? 

My understanding is that both me & my mother can buy seperate properties to claim exempltion.

2. I have another property in City Y which is jointly registered in mine & my wife name. Will there be any issue when I am claiming exemption for my portion while  buying another property (re-investement from sale of  above property in City X)?

My understanding is that, upto 2nd property is allowed to claim exempltion under section 54.

So in the end. After the sale of property in City X, my mother will be re-investing her full share to buy one property & I will be re-investing my full share to buy one property (along with 1 another property jointly owned by me & my in City Y). And overall there will be no tax for me to be paid from sale of property. Please confirm.

Thanks in advance.

(City reference is just an example to distinguish 2 current properties)