Wife is cheating?

My wife and I have been very rough relationship and more so recently. We never had sex since last october
She is constantly on business travel. For her dec 29, 30 travel she insisted that I accompany along with our five year old. However she carried sanitary napkins and appeared to be having periods. We returned home on Dec 31. Suddenly on Jan 1st she showed sudden interest and by afternoon we had unprotected sex as I thought it was a safe period. She said we will have this every day and next day left again to a business trip. After her return our daughter started saying that her mother told that she will be having a baby sister in mummy's tummy. I am confused. Is that possible?

With good reasons, you seem to be afraid that the baby is somebodys else's, but that your wife wants you to believe that the baby is yours. When the baby is born, you can have a DNA test made, and then you can be 100% sure whether the baby is yours or not.