Can women pray alongside men with a barrier?

Firstly: 

If a woman
prays alongside a man but there is a barrier between them, such as a wall,
or a gap which is wide enough for a person to stand and pray there, then the
prayer is valid according to the majority of scholars among the Hanafis,
Maalikis, Shaafa’is and Hanbalis, but they differed with regard to a woman
who prays beside a man with nothing separating them. The Hanafis are of the
view that she invalidates the prayer of three men: one to her right, another
to her left and a third behind her, subject to conditions that they
mentioned, which may be summed up by saying that if the woman is desirable,
has reached the age of seven years or is of marriageable age, with some
variations in the madhhab on this point, and she joins in a regular prayer
with a man, which includes bowing and prostrating, and they join together
simultaneously in the opening takbeer and the prayer, and the imam intended
to lead women in prayer, and other details which may be referred to in their
books. 

See
al-Mabsoot (1/183); Badaa’i’ al-Sanaa’i’ (1/239); Tabyeen
al-Haqaa’iq (1/136-139). 

Al-Nawawi
(may Allaah have mercy on him) said, discussing the difference of opinion on
this topic and summing up the Hanafi view: If a man prays and there is a
woman beside him, that does not invalidate his prayer or hers, whether he is
leading the prayer or praying behind an imam. This is our view and it was
also the view of Maalik and the majority. Abu Haneefah said: If the woman is
not praying or she is offering a different prayer than him and is not
praying with him, his prayer and hers are both valid. If she is praying with
him – and in Abu Haneefah’s view she cannot be praying with him unless the
imam intended to lead the women in prayer too – then if she joins the prayer
and stands beside a man, the prayer of the men who are standing on either
side of her is invalidated, but her prayer and the prayer of the man who is
beside the man who is beside her are not invalidated, because there is a
barrier between her and him. If she is in the row in front of him, the
prayer of those who are beside her and behind her are invalidated, but the
prayer of those who are beside the ones who are beside her is not
invalidated, because there is a barrier between them. If the women’s row is
behind the imam and there is a row of men behind them, then the prayer of
the row behind them is invalidated, but by analogy the prayer of the rows
behind that row is not invalidated, because there is a barrier. But we say
that the prayer of the rows of men behind them is invalidated, even if there
are a hundred rows. If she stands beside the imam, then the prayer of the
imam is invalidated, because she is next to him, and his view is that if the
prayer of the imam is invalidated, the prayer of those who are praying
behind him is also invalidated, and her prayer is also invalidated, because
she is one of those who are praying behind him. 

This view is
based on weak evidence and this argument has no basis. Our view is that the
prayer is valid unless there is sound shar’i evidence to prove that it is
invalid, and they do not have such proof. Our companions drew an analogy
from her standing in the funeral prayer, which is not invalidated in their
view. Allaah knows best which is correct, and to Him be all praise. He is
the Source of strength, guidance and protection. End quote from
al-Majmoo’ (3/331). 

But if there
is a barrier, the Hanafis agree with the majority that it does not
invalidate the prayer of either of them, as it says in Tabyeen
al-Haqaa’iq (1/138) 

Secondly: 

Undoubtedly
the Sunnah is for the women’s rows to be behind the men, as was the case at
the time of the Prophet (peace and blessings of Allaah be upon him).
Al-Bukhaari (380) and Muslim (658) narrated from Anas ibn Maalik (may Allaah
be pleased with him) that his grandmother Mulaykah invited the Messenger of
Allaah (peace and blessings of Allaah be upon him) to a meal that she
had made for him, and he ate some, then he said: “Get up and let me lead you
in prayer.” Anas said: I went and got a reed mat of ours that had become
blackened from long use, and sprinkled it with water. Then the Messenger of
Allaah (peace and blessings of Allaah be upon him) stood, and the
orphan and I stood behind him, and the old lady stood behind us, and the
Messenger of Allaah (peace and blessings of Allaah be upon him) led us
in praying two rak’ahs, then he left. 

Al-Haafiz
said in al-Fath: This hadeeth teaches us a number of things… that
women should stand behind the men’s rows, and a woman should form a row on
her own if no other woman is present. End quote. 

But if what
you describe happens, and a woman is praying alongside men, the prayer is
valid, praise be to Allaah.

And Allaah
knows best.