In short, you are not financially responsbile for a child who is not your biological child unless you have adopted this child. In that case, you would have full rights and obligations to that child.
Your are not financially responsible for your fiance's child. Your attempts to resolve the disputes with his child's mother has not worked. Get a order for visitation in place. Until such is in place the child's mother will continue to play games. But, remember that a custody dispute will likely become drawn out and that what you desire - adherence to a set schedule, will also be enforced against your fiance.
The court will not utilize your income to determine your husband's child support obligation for a child that is not yours. Relative to a lawyer in the area I can provide you with a name of an attorney if you contact my office.