Is it permissible to study in a mixed educational centre with better qualified teachers, when there is another centre where there is no mixing but the teachers are less qualified?

Firstly: 

In the answer to question no. 1200 we
explained the prohibition on free mixing and the negative consequences that
result from it, especially when it happens among youth in educational
settings. 

Secondly: 

in the answer to questions no. 70223
and 127946 we explained that in countries in which
the people are faced with free mixing in most areas of life, especially in
educational institutions and work places, there is a concession granted to
them in that regard which is not granted to others, based on the fiqhi
principle that “whatever is prohibited so as to bar the means that may lead
to evil may be permitted in cases of necessity and where doing so serves a
greater interest.” 

However care should be taken to guard one’s tongue, lower
one’s gaze and avoid anything that may be a cause of temptation. 

Thirdly: 

This is in general terms, in places where this problem is
widespread and the Muslim is not able to change it. But in specific terms,
if a Muslim is able to enrol in a school in which there is no mixing, or in
an education centre or private classes in which the genders are separated,
then he must enrol in such classes, so as to avoid trouble and ward off
temptation, and so as to adhere to the limits set by Allah, may He be
exalted. 

But if that is not available, or it is available to some
extent but there is a great difference in the educational level between the
two options, and he fears that he may be adversely affected or may miss out
on some benefits because of that, then in that case there is a concession
allowing him to enrol in that which is more beneficial to him, even if there
is free mixing in that place. However it is essential for him to denounce
the evil as much as he is able to, and to adhere to his religious commitment
and good manners, by remembering that Allah, may He be exalted, is always
watching. So he should guard his tongue, lower his gaze and avoid as much as
possible places where there is mingling and direct interaction. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was
asked: What is the ruling on a woman going to a male doctor to treat her,
when there is a female doctor in the same specialty? 

He replied:

If the specialty is the same, and the man and the woman are
equal in terms of their skill level, then a woman should not go to the male
doctor, because there is no need to do so. 

But if the man is more skilled than the woman, or more
specialised, then there is nothing wrong with the woman going to him, even
if there is a female doctor, because this is a case of need, and in case of
need such things are permissible.

End quote from Fataawa ‘Ulama’ al-Balad al-Haraam (p.
693) 

But if he is a person who fears that he may be tempted and
fall into sin, then he does not have the right to do that, because
preserving one’s religious commitment takes precedence over all other
interests. In that case he should leave these educational centres for the
sake of Allah, and enrol in a place that pays attention to separating the
sexes, even if its level of education is lower. Then he should strive hard
in his studies and think positively of his Lord, when he refrains from
attending the mixed institution for the sake of Allah, for whoever gives up
something for the sake of Allah, Allah will compensate him with something
that is better for him than it. 

Please see the answer to question no.
50398 

For more information, please see also the answer to question
no. 128996 

And Allah knows best.