I am confused on the ARM Rider. Are these required for 2nd mortgages?

Depends on what ARM rider you are talking about. Without reviewing the language on the specific rider you are referring too - it is hard to say.

The reasons we put an ARM rider in place was because the mortgage we used referred to a fixed rate only (this could have been Fannie Mae's standard mortgage now that I think about it?) Whereas one of our other loan systems lets you choose if the rate is an arm or fixed and prints out accordingly on the mortgage.

So if it amends the mortgage it wouldn't have to be recorded with the 2nd mortgage?

A 'mortgage', 'deed of trust', or 'promissory note' is a contract. A 'rider', 'modification agreement', or 'allonge' is an amendment to a contract. If the contract document must be recorded in order to have the legal effect you desire, then it stands to reason that any or all amendments would have to be recorded in the same manner for the same reason.