Daughters responsibility looking after widow ?

Unfortunately neither the son nor the daughter can be compelled to look after the mother and take care of her nor any heir can be compelled to relinquish his/her share in the property in favor of the mother. This is a matter of conscience and understanding. Legally the mother can only seek maintainance from the sons and daughters if she is unable to maintain herself from the income she is getting from the property in her name. You can have the good offices of some relatives who will help to resolve the matter amicably.

I completely agree with Adv. Archana

Family Settlement may be the best solution .

You three kids do not have to sign any papers so that your mother enjoys your father's property.  Till someone contests for a share, by mutual understanding you all can do whatever you want with that property.  If you are kind enough to forego your shares for mother's sake nobody can prevent her from enjoying that property, unless a claim arises in the form of a suit in future. If we go by the facts mentioned by you, the only litigant seems to be the sister who does not want to sign documents. Let her claim her share by contesting in court.  If she alleges that she has share in such and such property she has to show what is the property.  You do not reveal what your father left. 

After exhausting the said property for the maintenance of your mother if she still needs maintenance, such maintenance shall be paid by all the four of you equally.  Or if the amounts left over by your father is inadequate to meet her maintenance, your mother can file an application in Maintenance Tribunal U/s.4 (1) (i) of  Maintenance and Welfare of Parents and Senior Citizens Act, 2007 claiming maintenance from that sister alone. 

Even now such application can be filed so that she comes forward to have an understanding with all of you about her liabilities with respect to your mother.

I have nothing to do with the aspect who has to look after the maintenance of your mother. That is your personnal problem.  I can talk about only legal aspect.  As per law as your father died intestate (without writing will) you all i.e. four children and your mother equally are entitled for the properties. since there are disputes in your family, you have to file succession suit in the local court and you have to distribute the properties. for the time being somebody of you has to look after the maintenance and welfare of your mother. Any way your mother is entitled for her maintenance, apart from her share.