It's as complicated as you want it to be. If you want to make it easy, make a decision to not vaccinate her again, for anything. There are a lot of educated parents who have put many, many hours of research into vaccines, who have decided to completely stop vaccinating. You do not need to finish any shots.
Practice saying, "No vaccines today" before you see the doctor again. Does her father have the legal right to make medical decisions for her? If not, don't worry about convincing him. You could even tell him she got the vaccines, if he doesn't have a legal right to access the medical records.
If you decide to skip some or all vaccines, your life will be easier if you do not discuss that with anyone in real life. It's nobody's business but yours.
I am a VERY firm believer in doing ones OWN research.
I would say you and your partner need to sit down and talk about this. He needs to be able to voice WHY he feels this way, you need to voice why you feel how you do, then you need to educate yourselves together. Its not about who's right or wrong, but whats right for your ENTIRE family.
Plus if you feel this strongly you'll want the support of science, and information behind you so you can stand behind that choice and not appear to be reacting from fear alone. Its hard to respect the choices of someone who is not researched in a topic and reacts from fear. That means for BOTH sides.