This is the whole problem - it isn't, not really. The reason for the second vote is to assume that people now know much more about the implications of it all than they did in 2016. If the second vote was again Leave then, like all the other Remainers, I'd have to swallow it and accept it however much I hated it.
I'm sorry, but I have never bought this argument. When the referendum was called it had to ask a simple question i.e. in/out. There was no option for any shades of grey. It's true that people didn't know exactly what the terms of leaving would be, but it was IMPOSSIBLE for anybody to know this at that time. People cast their votes on the basis of what they did know, what the government told them and what their own experiences told them.
There was also no question raised at the time to suggest that the government would act on the result and would then check with the people whether the terms were OK via another referendum. They could have done so, but chose not to. Was it perfect? No, but could it have been any better? Probably not. Neither side was entirely truthful, but in the end it was a simple choice for us to make, and the result was perfectly legitimate. We should now be making the best of it, and politicians should be enacting the will of the people. There is no excuse not to, since they asked us for a steer on what they should do, and the referendum result was that steer. The fact they didn't like it is their problem not ours.