Electronic – RF amplifier, why don’t two cascaded amplifiers work

I would expect the gain-bandwidth product to be a constant, but it's worth comparing the two on the bench before designing it in (I suggest measuring both the gain-of-10 -3dB point and the gain-of-0.1 -3dB point to have a point of comparison with the datasheet limits).

Note that the slew rate is typically a fairly good 5V/us, but you'll run into that at high amplitudes.

To take Glenn W9IQ's answer and make it more specific, you should check the data sheet for the spec Input Common Mode Range. For this op amp, with +/- 15 volt supplies, the allowed range is a minimum of +/- 12 volts. In other words, it is not spec'ed to operate with the inputs within 3 volts of either supply (at +/- 15 volts). Granted, you are not using +/- 15, but then again the op amp is not characterized for any other power supply, which should be a warning flag. It will probably do OK at 0/15, but it may not. Assuming that it will work, you still should assume that the inputs must be within the range of 3 to 9 volts.

In other words, your op amp is completely unsuited to the use to which you are putting it. You need an op amp with rail-to-rail inputs, or at least with an input range which includes V-. A cheap example of such an op amp is the LM324.

Even if you do this, there is something you need to keep an eye out for. Your diagram shows the low end of the shunt resistor at ground, and the low end of Rg at ground. If your current is high (let's say, an amp or more), and the shunt is not placed directly next to the op amp, the current will flow through other wiring before being referenced to ground, and this will produce an apparent scale factor error. Worse, if there are other high currents running around your system, they may also be detected to some degree. You may see inexplicable output offsets and other weird effects which reflect those unacknowledged currents. Or maybe not. But depending on what else is going on in your system this may be a problem.