I was going to say the same thing. The circuits on the boat for each cord are (or should be) separate. So this tells me that when you hook up both cords and the breaker blows, the fault is on the shore side.  Check out the cords to eliminate any problem there. Then get the marina to check their system.

Something is definitely wrong on both sides, the dock and the boat. The ABYC Rule is that there cannot be two sources of power for the same circuit.  So if you have one cord plugged in it can power both circuits,  but if you have two cords plugged in there should be a transfer switch that isolates one circuit from the other.  ABYC rules also say that the neutral (white ) wires shall not be connected on the boat for the two sources of power, so when one power cord is plugged in the neutrals for both circuits are connected, but when two cords are plugged in the neutrals should not be connected. There should be a transfer switch that connects or disconnects the two depending on whether or not both cords are plugged in. I suspect that this switch is defective.  When you plug in one 30 amp cord, it should power every AC circuit on the boat. When you plug in the second power cord the switch should isolate one circuit from the other.  It’s not doing that so the breakers trip. I know I sound repetitive but it’s an important and subtle point.

However, as someone else said I also suspect the power outlet on the dock may have the black and white wires switched, in other words the polarity is wrong.  Any competent electrician should have a simple device in his kit that checks polarity.  In fact you can buy one at any hardware store for a few bucks.  You simply plug it into any three prong AC outlet and it has lights that indicate if the polarity is ok or if there are any ground faults in the circuit.

You need to have an electrician check out your boat and the dock power. This should be an ABYC certified marine electrician. Any old electrician will not know the differences between shore side and boat wiring.