You might find it easier to first gain up the 650mv output x15 or so, to get near to 10V output from it, as a first stage.
You might need to do this in 2 stages, with 2 opamps, x5 and x3, in order to keep within the limits of the Gain Bandwidth Product (GBW). For example, if your device has a 100MHz GBW, then at gain of 5, it only has a 20Mhz bandwidth. This is the -3dB point, so it actually starts to roll off its gain way earlier than that, like around 100kHz or 200Khz or so. This is why you often see high gains done in multiple stages.
Once you have the output gained up to 10V p-p, then you can use the digital potentiometer to control an inverting opamp as an attenuator, to attenuate the signal by 20dB or so. This will give you 0-10V output (approx). You have to be careful here too, because you are attenuating x10, and you still have to contend with the GBW product of this stage. Furthermore, you don't want the signal going through you digital pot, which does not have the bandwidth you need.
You could also forgo that, and just come up with a VCA (voltage controlled amplifer) but you'll need to design carefully to get the performance you need.
You'll also need your opamps to have very high slew rates for these speeds at 10Mhz and 10V output. Here's why:
Consider that your opamp is running fine, not slewing, and getting a nice sine wave output.
Then

.
The time derivative of the output is

and the maximum value of

occurs when

,
i.e. when the angular frequency at time t is an integer multiple of pi.
It is here that

and

and this cannot exceed the slew rate of the opamp.
so

, and
the maximum frequency and voltage that the op amp can output without slewing is:

In your design, Vp = 5V and fmax = 12.5Mhz, so 2*pi*12.5e6*5V = 392699082 V/s slew rate, or 393 V/us (as you'll find it on the datasheets in V/us). So you'll want your final stage opamp to have a slew rate of at least 1.5 to 2 times that, just to be safe, or 600 to 700 V/us
And finally, you'll also need to consider the Full Power Bandwidth (FPBW), which is the maximum frequency the opamp can put out with it's peak voltage equal to the clipping voltage (the Vout(min) and Vout(max) "rails" ). Going beyond this frequency (FPBW), the opamp will start full slewing and will reduce it's output voltage to a peak voltage of slewrate/4f. The peak output is inversely proportional to the frequency and the slewing output is not pretty.. You don't want to operate in this region, so you should seek it out on the datasheets

There was another recent thread about higher frequency op amps, and many "young players" look at the GBW and don't consider the slew rate, but the slew rate is equally important and needs to be considered along with GBW, so I thought I'd put the simple math out there in this thread for you and anyone else to understand the GBW, slewrate and FPBW better.
So, your first high frequency design is not so simple, as you can see. But you can learn from it.
Cheers!