My kid's mother will not let them sleep in their own bed. From the first day they came
Home from the hospital she has had them sleeping in our/her bed. What harm and problem's will this cause my kid's later in their development/life ?

Probibly none. But it sure limits the intamacy between you two and hinders your quality of sleep. They may also put up one heck of a fight when she does decide they need to sleep on their own.

This will not cause any problems for them. Many family co sleep including mine. However if both parents do NOT agree on this, it will not work. You need to talk to her about it and be honest with yourself and her as to why you do not want the children in your bed.