If I marry again my daughter will not be mahram to that man. It will be difficult staying in the same house for my daughter where she will have a non mahram all day long

No who said if you marry your daughter will be na mahram. He will be her father (step father) and according to Islamic Shariya step father and stem mothers are same as real father and mother. They are completely Mahram and all the children from another Husband or wife are brothers and sisters and they are Mahram for each other. But about cousins the rule is same as if they are real cousin or step cousins both are na mahram.