A few suggestions:

1. Take pictures constantly - not just to increase the chance you happen to 'grab one', but people eventually forget the camera is there if it's out constantly. You lose being able to capture the moments when the only time they see the camera is that special moment.

2. I tend not to ask people to move, but I re-position myself. If there is glare from a window, you should be able to move more parallel to the window and reduce the glare. Crouching low or shooting from higher than normal is another way to change the angle of the light and possibly get a more interesting perspective.

3. I'll ask for at least one or two posed shots during a 'lull' in the 'action'. This way, even if none of the 'natural' ones work out - I've got something. If the subjects are already really comfortable with you, sometimes the posed ones can be the best shots.

4. Scope out the 'good spots' you think would make a good picture (an interesting background like a rose garden, a particularly well lit area) and keep an eye there for good shots. Lots of people are naturally drawn to the more aesthetically pleasing areas anyway - it's just a matter of catching them when they're there.

5. Set the expectation that you're not there to embarrass anybody if somebody is acting nervous. Be upfront, honest, and confident. You'll be taking pictures and that if somebody doesn't want their picture taken that it's ok, but you're sure they would like the pictures. Once they're comfortable around you, it'll make your life easier.

6. Learn to get your posed shots looking natural. Working with people is tough. Be confident and direct them in ways that look natural and good to you, not that feel natural to them - there may be a difference. This was something @JayLancePhotography was talking about once, actually. Position your models so that they look natural. A position where it may look like they're stretching or 'caught' in a kiss or any other pose that looks 'natural' and 'sudden'. It may be rather difficult to get your model to hold this position intentionally for a photograph - it could feel very unnatural. But if it looks natural to the camera, that's what matters. So you shoot for what looks natural to you - you can't just tell your subjects to 'act natural'.