He wants her as a second wife without telling the first; should she accept?

Firstly: 

You should choose for yourself a man who is of good character
and religiously committed, as the Prophet (blessings and peace of Allah be
upon him) said: “If there comes to you one whose
religious commitment and attitude pleases you, then marry [your
female relative who is under your care]
to him, for if you do not do that, there will be tribulation on earth and
much corruption.”Narrated by at-Tirmidhi (1084) from the hadeeth of Abu
Hurayrah (may Allah be pleased with him)’classed as saheeh by al-Albaani in
Saheeh at-Tirmidhi. 

This may be found out by researching about the man and asking
his friends and neighbours, and the imam of his mosque; you should not base
your decision on emotions or unverified claims. 

If you are fortunate enough to find a man who is of good
character and is religiously committed, then you have been blessed with
something good. This is the one who is expected to be fair and just, and to
fulfil duties and obligations. 

Secondly: 

You say that this suitor lives far outside the city and you
are afraid that he will not be fair. This may be interpreted in two ways: 

1.That you want your full right
to a share of his time and you are afraid that he will not be fair, and that
he may be unfair towards you with regard to this right. This possibility is
very likely if he does not tell his first wife about the marriage, because
it will be difficult for him to give you the rights that are your due and to
explain why he is away from his home every day or night. This is what
usually causes problems and conflict, and may lead to falling short with
regard to your rights.

2.That you do not want your
rights in full and you are content with him coming to you every now and then
whenever it is easy for him. In that case not telling his first wife may be
better, and in most cases it will be possible for him to organise his life
properly with both of you, and he can use double entendres if he is asked
about where he is going or why he is late.

You have to be clear about your attitude and your wishes. If
you want to have your rights in full, then we do not advise you to get
married until he tells his wife and you think it most likely that he is able
to deal with problems and achieve fairness (in his treatment of both of
you). 

If you give up your right to a share of his time, then you
can marry him without him telling his wife. 

Whatever the case, you should not tell his wife anything;
rather this is a matter to be handled by the man himself. If you tell her
then it may spoil the relationship between them. Moreover, you have been
entrusted with this secret that has to do with him only, and you do not have
the right to disclose the secret without his permission. 

You should be prepared, if the marriage takes place and you
see some shortcoming in his giving his first wife her rights, to advise him
to be fair, which is the way of earning Allah’s pleasure and attaining
happiness and stability for you both. 

And Allah knows best.