The property bequeathed by your father belongs to the beneficiary after his death that is, when the Will becomes enforceable.

You can ask the joint beneficiaries to enforce the Will by applying for transfer of revenue records from your father's name to the names of the beneficiary, if they don't co-operate then you can approach court to get probate of Will in order to get your share mutated accordingly.

As far as your mother's Will, it will become operable only after her lifetime and she can cancel it anytime during her lifetime.

Your mother's name in FDRs along with your sister for the money you own can be disputed by you by filing a suit for declaration to declare that money belongs to you by providing documentary evidences.

If the plot was gifted to you by your mother through a registered gift deed, it became your absolute property. A Gift Deed, once registered, is valid.

2) the FDRs are in joint names (you and your mother), they are generally seen as being with "either or survivor" clauses. However, if you can prove via bank records that the source of the money was your own income, you can claim sole ownership.

3)Collect all bank statements showing that the FDRs were created from your own hard-earned money to rebut any claim that it was your mother's or father's money.

4)if you had paid full consideration fir purchase of plot you can file declaratory suit that you are absolute owner of plot 

Your sister’s insistence on making your mother a joint holder in your assets is likely a strategic move to influence inheritance. As a joint owner, your mother had a legal share in the plot and FDRs. If she had passed away without transferring them to you, that share would have formed part of her estate and been distributed among all legal heirs—including your sister—according to succession laws or your father’s Will. By having your mother gift the plot to you, that asset may now be solely yours, provided the gift deed is valid and irrevocable. However, the jointly held FDRs could still be contested. After your mother’s death, your sister may argue that half the FDR amount belongs to your mother’s estate, especially if the funds were held as "joint tenants" with survivorship benefits or as "tenants-in-common." She could challenge your father’s Will if she believes she was unfairly treated, potentially delaying distribution and creating legal hurdles. To protect yourself, ensure all gift deeds and nominations are clear and legally sound. Consulting a lawyer to review these documents and your father’s Will is essential to preempt future disputes.

The property belongs to you the sister doesn't have to be included necessarily in every transaction. After your mother she can claim a share of the property if your mother is a share holder. Therefore do not make your mother a sharer in any property you purchase. The will can be challenged as it is a weak document.

She may be having a hidden agenda as you apprehend, you can strongly object to the proposal of joint FDR account because it is your money.

The reason why your mother is kept in joint names is for mother financial security 

further on mother demise intestate the money would devolve on you and your sister equally 

mother can by will bequeath money lying to your sister