I see.
Well, the simple answer is that marrying their mother doesn't give you any extra rights of parental responsibility by virtue of being a step-parent - you can't make medical decisions for the kids, change their names, consent to international travel, or change their school enrollments. You would need to adopt the kids to gain parental responsibility, and you would need biological dad's consent to adopt them.
For the record, who the kids live with has no bearing on parental responsibility, and in fact, it's pretty standard for both parents to have equal shared parental responsibility (or 'decision-making') even if they live full-time with one parent or the other.
Also, for clarity, child support is a legal matter separate to custody and parental responsibility. If dad is assessed to be paying child support, then mum should take this up with the child support agency so they can pursue it on her behalf.
Final note, dad doesn't have to comply with mum's requests, and mum doesn't have to comply with dad's requests. Not liking the other's non-compliance doesn't mean one of them should lose parental responsibility all together.