Should she appoint a company to do Hajj on her behalf when she does not know whether they will do the rituals as they should be done or not?

Firstly: 

We ask Allah the Almighty, Lord of the
mighty Throne, to heal you of your sickness by His grace, generosity and
kindness, a healing that leaves no sickness behind. 

To proceed: 

If a person is sick with an illness for
which there is no hope of a cure (and which prevents him from doing Hajj),
then he may appoint someone else to do the obligatory Hajj on his behalf, on
condition that the proxy has already done Hajj for himself. 

Please see the answers to questions no.
83765 and 111794 

Secondly: 

The basic principle with regard to these
companies that do Hajj and ‘Umrah on behalf of others is that they are to be
trusted, because trust is a basic factor in their continuing to operate, and
they are keen for their companies to keep going. The people involved in any
project are usually very keen to do their work properly so that people will
come to them and will not think badly of them, thus shunning them and going
to someone else. This is the least that can be said with regard to the basic
principle. 

Nevertheless, you should be careful with
regard to your acts of worship and strive hard to discharge your duty
properly (by making sure that everything is in order), and you should not
rely in such matters on anyone except people who you know or think most
likely will do the job properly, either because you know that from
experience or you have heard that from trustworthy people who know the
persons involved. 

Then if you have tried your hardest in
that regard and you think it most likely that the proxy is trustworthy, then
you do not have to examine him closely and find out if he has fulfilled the
trust or not, because the basic principle is that he will do it, especially
with regard to acts of worship, unless you see something about him that
gives rise to doubts concerning him. 

Shaykh Ibn Baaz (may Allah have mercy on
him) said: 

The basic principle is that in such
matters the one who takes it upon himself will usually do it. This is what
usually happens; there may some cases where trust is betrayed, but in most
cases the proxy will do it. But if a person wants to be on the safe side and
does another Hajj, that is better, and it comes under the heading of the
hadith “Leave that which makes you doubt for that which does not make you
doubt” and is safer. End quote.

http://ar.islamway.net/fatwa/43807 

Whatever the case, we do not advise you to
deal with such companies of which you do not know anything and of which no
trustworthy person who knows about them has told you anything good. 

We know that in every country and in every
place there are people one knows who are residents or travellers to that
country who could do these things on your behalf, so try hard to look among
those around you or those whom you know for someone whom you can appoint as
your proxy to do that on your behalf, or who can appoint a trustworthy
person who is able to do that. 

Thirdly: 

If the sick person appoints someone to do
Hajj or ‘Umrah on his behalf, then he should appoint someone who is
trustworthy and knows how to do the rituals; he should not appoint someone
who is not trustworthy or is ignorant. 

If he appoints someone then it becomes
clear that he is not trustworthy, then if he appointed him to do the
obligatory Hajj and it turned out that he did not do the rituals as they
should be done, and he was careless in carrying out what he had been
appointed to do, then the proxy is liable for the costs of this Hajj,
meaning that he (the one who appointed him) may ask him to pay for the cost
of this Hajj, and it should be taken from him, then he (the one who
appointed the proxy) appoint someone else who is trustworthy and knows how
to do the rituals, to perform Hajj on his behalf the following year. 

If he appointed him to do voluntary Hajj,
then it turned out that he was not trustworthy and did not do the rituals as
they should be done, then he (the proxy) is liable but the one who appointed
him does not have to make arrangements for another Hajj on his behalf the
following year. 

Shaykh Ibn Baaz (may Allah have mercy on
him) was asked: 

There is a person who gave some money to
someone to do Hajj on behalf of his mother, and he thought that he was
trustworthy, then it turned out that this person was involved in things that
are not right, and he is asking what he should do. 

He replied:

The one who wants to appoint someone else
to do something on his behalf has to look for that person and find out
whether he is trustworthy and righteous. If the Hajj was obligatory, he has
to make up for it by doing another Hajj. If the Hajj was in fulfilment of a
person’s last wishes, with the costs to be paid from his estate, and he (the
heir) gave that task to someone who was not trustworthy, then to be on the
safe side he should do it again, because he was not careful; rather he was
heedless. But if it was a voluntary or recommended Hajj, and there was no
final instructions from someone who passed away – rather he wanted to do a
voluntary deed and earn the reward – then he does not have to do anything,
although if he wants to do it again, there is nothing wrong with that. 

End quote from Majmoo‘ Fataawa Ibn Baaz
(16/420-421) 

Fourthly: 

The scholars differed with regard to doing
a voluntary Hajj or ‘Umrah by proxy. Some of them regarded that as
permissible, if the one who appoints the proxy is unable to do it because of
old age or sickness for which there is no hope of a cure, and the proxy has
already done the obligatory Hajj on his own behalf. This is the view
favoured by the scholars of the Standing Committee and by Shaykh Ibn Baaz
(may Allah have mercy on him). 

Others are of the view that this is not
allowed, and this is the well-known view of Shaykh Ibn ‘Uthaymeen (may Allah
have mercy on him). 

Please see the answer to question no.
41732

Shaykh Ibn ‘Uthaymeen (may Allah have
mercy on him) issued a fatwa in which he granted a concession allowing a son
to do a voluntary Hajj on behalf of his father, at the father’s request. 

He (may Allah have mercy on him) was
asked: 

My father has asked me to do Hajj on his
behalf this year, a voluntary Hajj, because he did Hajj once. He is
financially able to do Hajj, but is physically unable due to poor health.
Can I do Hajj on his behalf, knowing that I have already done Hajj for
myself? 

The shaykh replied: There is nothing wrong
with doing Hajj on his behalf in this case. 

End quote from al-Liqa’ ash-Shahri
(62/21). 

And Allah knows best.