Can a woman satisfy both Allah and her husband, especially in the month of Ramadan? Would her Du'a or prayers not be accepted if she neglects her duties towards her husband (e.g. sexual intercourse) for being fully submissive to Allah?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

There is no contradiction between obeying one's husband and fulfilling Allah's Commands and Orders regardless of whether that is in Ramadan or in other months. It is obvious that the fasting person should refrain from eating, drinking and all other things that break the fast including sexual intercourse. It is forbidden for the fasting man to have sex with his wife during the days of Ramadan (i.e. from dawn to sunset). It is forbidden for the woman (his wife) to obey him in such a thing.

As for the nighttime, Allah Says (what means): {It has been made permissible for you the night preceding fasting to go to your wives [for sexual relations].} [Quran 2:187]

So, it is lawful for the husband to enjoy his wife and have sex with her during Ramadan nighttime and it is mandatory on the woman to obey him as his obedience in such a matter is an obedience to Allah. However, during the daytime they should both resort to worshipping Allah.

Allah knows best.