Uneven (10 dB) RF Power Splitter/Combiner
The splitter you currently show in your circuit appears to take in power X and distribute it to one port at X/2 and another port at X/2 i.e. there is no power loss. Just to confirm with real numbers, 16dBm enters and two lots of 13dBm leave. 13dBm is half the power of 16dBm hence two lots of 13dBm is 16dBm i.e. no power wasted.

What you appear to want doesn't make sense as being something useful. A "10dBm power splitter" would effectively (or so it seems) take an input of 16dBm and produce two outputs each being 6dBm. The total power out would be 9dBm (i.e. 3db higher than 6dBm) and there would be a power loss in the splitter of 7dBm. That loss is just heat and wasted.

Why would a manufacturer make one of these?

Stick with the 3dBm splitter and put an attenuator in line to the mixer. You should easily be able to get an attenuator that suits.

EDIT - worked example of a resistive splitter that maintains impedances at 50 ohm









simulate this circuit &ndash; Schematic created using CircuitLab

With R1 at 5 ohms, the power to the antenna is 83% (an attenuation of 0.8 dB). To match the input impedance to 50 ohm, R3 must be 500 ohm and this attenuates the signal to the mixer by about 21 dB. 

You can mess with R1 and R3 to give different ratios but, to keep impedances correct: -

\$R_3 = \dfrac{1}{\frac{1}{50}-\frac{1}{50+R_1}} - R_4
\$