It is so difficult with twins. Can you take a friend who they're familiar with? It might even be better if you're not in the room if them you're this anxious. I think they prefer you not to give Calpol beforehand because they need to know the baby is their normal self after the injection. Calpol won't help much with the very short pain, and a temperature wouldn't kick in very soon anyway - afterward, like @whatwouldjasonbournedo says is fine. Despite what you say, I'd be tempted to get them done separately because it's so hard on you if they're both ill at once and you sound like you're on your own without back up.
Do either of the kids have allergies? Sometimes vacs involved traces of egg and kids can have a reaction.
If they get feverish (my DC1 had a raised temperature with MMR ten days after the jab, which is when the measles bit kicks in), give them Calpol, it lowers the temperature. If a temperature is really bad you can alternate between Calpol and infant ibuprofen every four hours to stay on top of it (as @whatwouldjasonbournedo says. Don't bundle them up too much or the temperature will get worse.
If you're anxious, they will feed off that. You sound phobic about this. The doctor fobbed you off, but who gives the jab at your practice? Could you speak to the reception team and explain you need support with this - always start with 'I know my children need their vaccinations, but...'. They will just think you are an anti-vaxxer muppet otherwise. There is a school of thought that a lot of anti-vaxxers are actually phobic about vaccinations and if you dealt with that anxiety better you might win some over. My surgery has two nurses do vacs together. Could you speak to one in the week before the appointment and explain your concerns. Or could a health visitor help you - explain how exhausted you were with the other jabs and get their sympathy. Could they speak to the practice for you. There must be someone who can help on the day.
A friend of mine's mum had a bad experience with her eldest child's MMR. My friend was her second child and she didn't give her the MMR. Friend got measles. Measles was so horrific that she didn't hesitate to get her third and fourth child done. If your kids got a bad reaction to the early jabs, that could be about what those jabs were for (eg whooping cough is part of both of those sets of jabs). Again, speak to an HV about it? Hope it goes better this time.