We can only omit "that" before a relative clause if it is not the subject of that clause. In #1, "that" is the subject of "that told me to say so"; it cannot be omitted. It is optional in #2.
...and I wouldn't, but I'd promote the person told (I was tempted to say 'tellee' but resisted ;-)) to make it the first word, using a dummy 'the one/person... etc': 'You were the one I told...'/'I was the one who told you...'/'I'm the one you should...'