She has a disability and is unable to do wudoo’, and her children refuse to help her to do wudoo’

Firstly: 

It is obligatory for the children to help their mother to
purify herself, because this is her right and is a duty upon them. Not doing
that means that they are committing one of the most grievous of major sins,
which is disobedience towards mthers. 

There is the fear that Allah may hasten the punishment for
them because of this sin. 

So they have to repent to Allah, regret what they have done,
apologise to their mother, ask her to forgive them, and strive hard to obey
her and please her, for this is one of the gates of paradise and they do not
know when it will be closed for them, at which time regret will be to no
avail. 

With regard to purifying herself if they refuse to help her: 

If a sick person is unable to do wudoo’ and cannot find
anyone to help him do it, even in return for payment, then he should do
tayammum. He may do tayammum using the bed on which he sleeps if there is
dust on it, or he can keep a vessel next to him in which there is sand or
dust with which he may do tayammum. 

Al-Bahooti (may Allah have mercy on him) said in Kashshaaf
al-Qinaa‘ (1/103): If the sick person who is unable to do wudoo’ for
himself can find someone to do wudoo’ for him or to do ghusl for him in
return for an appropriate payment and he can afford it, then he must do
that, because in that case doing wudoo’ is obligatory for him as it is for
one who is healthy. If he cannot find someone to do wudoo’ or tayammum for
him, because he cannot afford to pay or he cannot find someone to hire for
that purpose, then he should pray as he is. End quote. 

If the woman asked about here is able to hire someone to help
her do wudoo’, then she must do that.

 If she cannot afford it, then she should move on to doing
tayammum, because Allah, may He be exalted, says (interpretation of the
meaning): “But if you are ill or on a journey or any of you comes from
answering the call of nature, or you have been in contact with women (i.e.
sexual intercourse) and you find no water, then perform Tayammum with clean
earth and rub therewith your faces and hands” [al-Maa’idah 5:6]. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was
asked: If a sick person does not have any dust, can he do tayammum using the
wall or bed, or not? 

He replied: If the wall is made of “clean earth”, whether it
is rocks or bricks, then it is permissible to use it for tayammum. But if
the wall is covered with wood or is painted, if there is dust on it, then it
may be used for tayammum and there is nothing wrong with it, and he will be
like one who does tayammum using earth. But if there is no dust on it, then
it does not come under the heading of “earth” and cannot be used for
tayammum. 

With regard to the bed, we say: if there is dust on it, it
may be used for tayammum; otherwise it may not because it does not come
under the heading of “earth”.

End quote from Fataawa at-Tahaarah, p. 240. 

If she is unable to do tayammum, she may pray without wudoo’
or tayammum, because Allah, may He be exalted, says (interpretation of the
meaning):

“Allaah burdens not a person beyond his scope”

[al-Baqarah 2:286]

“So keep your duty to Allaah and fear Him as much as you
can”

[al-Taghaabun 64:16]. 

Thus it is known that it is not permissible for her to pray
without wudoo’ or tayammum so long as she is able to do tayammum. 

And Allah knows best.