Previous 2-parties paid TDS, after 3-party setup, should all pay TDS or 2-parties can continue?

I have purchased a flat and it is in the name of 2 people - me and wife. For say 5 installments (it is still under construction), we both paid TDS separately as per the govt norms. Now I have added my mother as the 3rd party in the sale agreement, and it will be like this in the sale deed at the end of the handover also. My question is: 1. Is it mandatory for my mother (who is not earning) to also pay TDS? (And the TDS will be split into 3 instead of the earlier 2) 2. If the above is true, how will the 'sum of previous installments' value be calculated now? (say the 2 parties had already paid 1.5 lakh till now. So, say for the current month's 21k as TDS value, should we have 1.5lakh+10.5k for myself and wife, and 0 for my mother)? (I know that the installment value will be split into 3, while the sale consideration value will remain the same for everyone). This will my mother's (3rd party) TDS accumulation would start with the current month only. 3. Or do I have to go backdated to pay TDS for all installments for my mother and then claim the excess from the govt?