Newbie Question

Since you are tripping the house GFI, not the breaker, see if you can identify the cause:

Turn off RV main breaker and unplug all appliances. Plug in and see if the GFI trips. If so, the problem is between your shore power cord male end and the breaker box.

If not, start turning on things until you identify the culprit.

Did you shut off the battery charger on the motorhome before plugging it in? That can be a big load in and of itself when you first plug in and it is bulk charging.

Are you certain the electric water heat and fridge are both off?
Is there anything else on that circuit in the house?

It's the GFCI on the MH that trips. But it also trips the breaker on my house.

I would start by replacing both GFCI, probably the home outlet first.

Also try turning off all breakers in the RV and see if it trips.
Then turn on one at a time starting with the main.
Post which trips the GFCI.

Most MHs are not friendly with GFI circuits. Find a non-GFI circuit to plug into. If you have an inverter/charger, you also need to set it to use only 5 amps from shore power. Make sure the water heater and fridge is off. Once you have established a good power connection, you can turn the fridge back on to cool down.

Just reread your post. Is the GFI popping in your house or the MH?