Definitely take a monitor - great for reassurance, and means you can put him to sleep in a separate room and to bed early and all sleep better but don't forget the electricity adaptor!
They now say you can take them swimming at any age, but they can be scared if there's a lot of water and people etc. so might not enjoy it too much!
The flight thing is fine too at 3 wks, some people from India have their baby here, get a same day passport and then fly straight back.
I wouldn't agree to anything other than the wedding though, because we took our 5wk old to the USA for 2 months, and it wore me out! Everytime you go anywhere you have to think what to take, then think when its feeding time, nap time etc. Even eating out was a pain! So just try and get them to let you stay in one place at home as much as poss while you're there. Plus you might feel dreadful after delivery as I did, and being a firsttimer makes things worse.
Oh, another tip - don't even try and get a photographer to take his passport photo. Just get the guidelines and do it yourself, lay him down on a white blanket when he's awake. He doesn't have to be looking at the camera but needs his eyes open and with mine, he started crying everytime I put him down at the photographers so we couldn't get his eyes open!