When I was heavily pregnant with ds1, I attended my dsis's wedding with no problems, and when pregnant with ds2, I got two wedding invitations from close friends - one for 4 weeks before my due date and one for 4 weeks after. The later one was in Aberdeen, and we lived over 8 hours away by train - but we went to both weddings - the first one I was heavily pregnant and had a 19 month old toddler in tow, and the second one, I had a 5 week old baby and a 21 month old toddler to cope with.
It would not even have occurred to me on any of these occasions to have expected the bride to change her wedding date to suit my pregnancies.
That said, though, neither my sister or either of my friends was expecting me to organise two parties for them and then help with the food for the wedding - I do think that the bride is being very unreasonable to expect the OP to do all of this when pregnant. I would offer to do the engagement party but would then explain that I wouldn't be able to help with the hen night and might well not be able to help with the food for the wedding - and if I did, I certainly wouldn't be able to organise it or do the bulk of it, but might be able to help put together some savouries or cut some sandwiches.
I suspect that your friend doesn't appreciate what late pregnancy is like, OP, or that babies don't work to the timetables that they are given - hence her thinking you will still be able to do the parties and food. But I do think you should consider going to the wedding - unless it is really close to your due date, of course. As others have said, book into a hotel close to the reception venue, and take things easy on the day - but you will still be there for your friend, sharing her day.
Tell your friend that you can't guarantee being able to do anything near your due date, because the baby might come early, or you might just not be up to doing much, but that you will do what you can.
Incidentally, I travelled over 90 miles from my home only 2 weeks before my due date with ds1, helped clean the outside of the train that was there for its naming ceremony, and got home again without any problems whatsoever.