I've watched this movie when I was young and all I can remember is, two kids meeting a fairy (it's not a traditional fairy though. He has a piggy nose so what I remember is, this fairy was abandoned from his world and was living by himself) and they were able to go into the new world I think. It was pretty scary for little kids to watch at that time. The most impressing scene was, the last scene: one of the kids, the older brother, woke in the middle of the night and find out he has the piggy nose as that fairy did. And I think that was the end of the scene. Does anyone knows the name of this animation?

Was the fairy kind of greenish - and fat?

Haven't seen this, but my searches keep bringing me to A Troll in Central Park - but I'm not sure if that fits your description exactly. I kind of remember a greenish troll / goblin type character with an actual pig nose... I'm trying to find it to see if that's what you're looking for...

I'm with aliseadoo here, it sounds like troll in central park, I have it on dvd and it sounds like what you are looking for :)