I need to get a few assumptions away so I can help. I am assuming we are working with 2 120vac cords and not 2 220vac cords, correct? What type connections are you working with, are they twist lock or do they look like regular 120v plugs? 3 prong or 4? And are you using adaptors of any kind?
Here is what I am thinking is wrong, I think the hot and neutral have been reversed in the pedestal, cord, or boat. With only one circuit on at a time, even though reversed, will work with out issue. When you turn both on it would create a hot to neutral short, tripping the pedestal breaker and not the boats main. The two circuits share the neutrals and grounds, but not the hot's. You can test and prove this. Take your multi-meter set to ACV. Start at the pedestal, this is where it depends on what type plug in, and I will assume you have a twist lock. There will be one slot that has a 90 degree turn in it, the others even though curved, are straight, this is the ground. Place one probe in this slot (the one with the 90 degree turn), you may have to wiggle it to get a good connection. At this point it depends on the configuration, the neutral should be the smaller and the hot should be the larger of the two remaining slots, again depending on the configuration, and is really not important yet. Take the other probe, and stick it in the smaller slot, the meter should read almost 0, may read up to 10vac, then check the other slot, it should read 120, again you may have to wiggle the probes to get a good connection. If it is the reverse of this, for now this is ok, just remember or write down which slot gave you 120, and which gave you almost nothing. Do the same test on the other outlet, it should be EXACTLY the same, this is the important part. If they are different, and I expect they will be, you have your problem, the hot and neutral's are reversed. If they check the same, plug your shore cords in, and check the boat end the same way. If they are different, then one of the shore cords are reversed. If they check the same, then it is reversed at the boat and we will get into checking that later.
If you look at the plug on the pedestal, there will be a number, something like NEMA L5-30R, and the shore cord, both ends, will have a number also, post those and I can tell you exactly what the configuration should be as far as to which one the neutral should hook to. In all cases, the ground is the one with the 90 degree turn.
Be very careful as you will be working with live systems that can seriously hurt you.
Also, during all this I am assuming you are actually tripping a breaker or breakers and not a GFCI. Is this the case? Also insure that the breakers are or are not GFCI breakers, GFCI breakers look different than normal breakers and should be marked GFCI............D...........
