The only differences between 2nd and 3rd in OD are that 2nd gear has the intermediate band applied and the High/Reverse clutch is not applied. When it shifts to 3rd. the intermediate band apply comes off and the high/reverse clutch is applied. It sounds as if the application of this H/R clutch is lacking in some manner... but that higher RPM's solve the problem. I'm going to guess you have a control pressure issue here - the best way to find out is to see with a pressure gauge. If there is low pressure, it could be a number of things... starting with the piston seal in the high/reverse clutch, a loose valve body bolt allowing leakage, a worn/leaking pressure regulator....even pump issues.... But that's my guess where your problem is. I'm guessing that higher RPM's will up the line pressure and completely engage this clutch. If true, that fact doesn't tell us much though, by itself.
I'm uncertain whether a leaky vacuum modulator could be a possible culprit. I tend to doubt it, but would be easy enough to test.
