My husband and I often have sexual intercourse late at night, and in most cases, I fail in observing the Fajr prayer. Does this make us sinful, knowing that this is the only time we can have sexual intercourse as we have to wait until our child sleeps?
Now, we are in Ramadan, if I woke up Junub (a state of Janaabah - post sex impurity), can I perform Ghusl (ritual bathing) and continue my fast?
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.
As for the first part of your question, you should know that delaying even a single prayer on purpose until its time has passed is worse than committing adultery, theft, and drinking alcohol according to the consensus of the scholars. (This was reported by Ibn Al-Qayyim at the beginning of his book As-Salah – The Prayer). In fact, it is considered disbelief according to some scholars. Having sexual intercourse late at night does not justify leaving the Fajr prayer intentionally until the morning. What prevents you from performing Ghusl and praying?!
If we suppose that you become too exhausted to perform the prayer in spite of trying in every possible way to wake up, then you are not sinful.
With regard to the second part of your question, if a person woke up after dawn in a state of Janaabah, his fast is valid as long as he had intended to perform the obligatory fasting from night.
‘Aa’ishah and Umm Salamah, may Allah be pleased with them, said, “At times, the Messenger of Allah would get up in the morning in the state of Janaabah after having sexual intercourse with his wives in Ramadan, and not because of wet dreams, and he would then [perform Ghusl and] fast.” [Al-Bukhari and Muslim]
As for the Hadeeth that was narrated on the authority of by Abu Hurayrah, may Allah be pleased with him: “Whoever gets up in the morning in a state of Janaabah should not fast”, this is either abrogated or referring to what is preferable when the fast is merely a voluntary one.
Allah Knows best.