Is it permissible to pay expiation (kaffarah) and fast the coming Ramadan and make up the missed days thereafter, knowing that I am pregnant and breastfeeding and fasting causes me hardship?

If you broke your fast for a number of days in the past Ramadan (definition) due to an excuse, and the excuse continued until just before the upcoming Ramadan, there is no blame upon you for delaying the making up of those days until your excuse is gone and you are able to fast. No expiation (kaffara) is obligatory upon you. What is obligatory is to make up the days you missed. It is permissible to delay making them up until the excuse is removed, as mentioned by Al-Shirbini in "Mughni al-Muhtaj."