Given your concerns about illness after the first vaccination and the fact the children were pre term, it might be helpful for you to speak to a doctor about why there was an issue with the first vaccine, check if they think medically that the next vaccines are ok to give, and on what schedule for best uptake. Also, if you are concerned about vaccines in general, they can provide evidence based information about advantages and disadvantages of different vaccines, and talk about the specifics for your children.
My child is immune suppressed and has been for several years. They have only just completed some of their vaccines which are normally all given by age 2, as it was more risky to give them than not at various points, particularly the live vaccines. That was specific to her heath. So for several years we have been limiting exposure to other people and relying on herd immunity, which is terrifying.
But her GP and Consultant were very helpful in listening to our concerns and giving thier advice with reasons why they were giving it and what was appropriate for her at each stage. We felt more in control of what was the best for her because we educated ourselves and took guidance from relevant professionals.
If the person for them GP practice has put you off vaccinating because of thier attitude, please report this back to the practice manager as it is likely to have an impact on multiple families, not just yours.