Salamun Alaikum,
In my opinion and purely based on verse 3:43 that you have cited, one cannot conclude whether this means pray separately with others in the same place of worship or intermingled with men. The verse simply speaks about devotion and then to bow with those that bow. All that can be implied is a congregational prayer of both genders at best (not necessarily intermingled).
Yes, I agree, women should be allowed to pray in the same mosques with men. However, gender separation can still be maintained despite prayer being performed in the same prayer hall. I know of many women that would feel uncomfortable praying along with unknown men and vice versa. I don't think that one has to prove a point by intermingling both sexes as I'm sure you will agree. I think there are many Mosques in which men and women participate in the same prayer congregation under one prayer leader and in the same prayer hall. Also in the Holy sanctuary of Ka'aba men and women are often seen praying together. (Possibly due to practical logistics given the multitudes of people as opposed to choice).
To say Friday prayer is only required for men is not supported by the Quran. The Quran clearly addresses 'Ya-ayyuh-alladhina amanu' (O ye who believe) with regards to a Friday congregational prayer in verse 62:9 which includes both men and women. There is no support from the Quran to limit prayers in Friday congregations to men alone.
I hope that helps.
Joseph.