In your description system the biggest lateral force will become on the Vessel Anchor.
The biggest lateral force in the Pipe will become on the intersection Vessel/Pipe.
The force distribution will be as follow:
The greatest force are on the down site vessel and will be come smaller in the up site
The greatest force in the pipe will become on the intersection to the vessel and the
forces will be smaller in the down site the pipe.
I think your problem is simple to calculate with Caesar. But you must look for the right
element lenght (lumped mass), the stiffness on the intersection and the mass distribution
on the vessel.
Use the UBC Spectrum.