You should consult an attorney. The court has to determine what is in the children's best interest. Depending on the circumstances the court can find the consent of the mother is not needed to allow the step mother to adopt.
Note that this answer is NOT a substitute for legal advice, nor does it create an attorney client relationship. Please consult with an attorney.
It is possible to adopt without the biological mother's consent; however, unless Child in Need of Services or the local police were involved in an incident involving the children at the hands of the mother, then you will need to have her parental rights terminated by a court. Then, you can petition for adoption of the step-kids; pending a home-study report by a licensed adoption agency. The process is likely to incur fees for court, attorney and agency of at least $2,500 if you have to have her rights terminated.
If I can be of assistance, please do not hesitate to call for an appointment.
veRONIca jarnagin, atty, pc
veRONIca jarnagin, atty, pc 317-253-7664 provides this response as general guidance and not specific legal advice. If you wish to receive specific legal advice for your situation, please call to schedule an appointment.