How does a wife make up nine days from the first Ramadan and the entirety of the second Ramadan, knowing that she did not fast them out of fear of her milk supply being cut off due to breastfeeding? Is she only required to make them up (qada'), or both make them up and pay expiation (fidyah), or only pay expiation? Is it obligatory to make them up before the next Ramadan, or is it permissible to postpone it due to breastfeeding?

Your wife must make up the nine days she missed from the first Ramadan (definition). If she delayed making them up while she was able to, then she owes an expiation for the delay. She must also make up the entire second Ramadan that she missed. If she missed it out of fear for her fetus, then she must make up the days and feed one poor person for each day from the father's money. She should make up all the missed days before the next Ramadan. If she delays making up the days while she is able to, until the next Ramadan begins, then a fidyah (definition) is obligatory for her for each day of the second Ramadan that she missed.