I am using the exact same pills as you; alesse 28...
I am currently finishing my third month.
All I can say is you are lucky, lol. My whole entire first month on alesse was horrible! I had the brown discharge (breakthrough bleeding) for the whole month... It wasn't until after I got my period and started a new pack did it go away...
So I would assume that your breakthrough bleeding will go away hopefully before the end of your pill pack, and considering you are on week 2, you only have close to 2 more weeks to go... And your trip is in 2.5 weeks. I think you should be good to go, don't worry.
And yes, the discharge you are experiencing is normal, don't worry about that either... If it get very heavy, or continues for some reason throughout your 2nd pack of pills... See your doctor, it could just be that alesse is not the right pill for you.
Take care.