Wow, how this must lay heavy on your heart.
I don’t know what to tell you, especially since your DH is not wanting to convert.
I can only offer this, lead by example.
my husband is atheist and will not convert. So, I lead by example and share interesting and happy information about the church. He knows how important this is for me and supports my journey. He also knows that our daughter will be raised in the church and he does not protest.
My husband has been damaged so much by his family (Southern Baptist) and others (he attended Wingate to be a minister and they treated him so poorly). So I believe all he needs is to remember God’s love, but in his time and God’s- not mine).
In regards to birth control, you can only control your own body and not that of others.
I’m sorry you are dealing with this and know that it will all make you stronger in faith.