ukbob, I think you are suggesting the little brother be totally disconnected from the internet. I suspect that's not the objective of MyLittleMute. But instead to block their use of FrostWire or limit its use in some way.
I suspect blocking of most ports outside those used by your browsers is possible via your router, though abilities of this will vary depending on brand & model.
With my internet service we have ability to block a port range via our settings with the ISP. Aim would be to block those ports above 1000 I'd suggest. Whilst this will not totally stop the use of LW, it will most likely cause some form of connection issues.
Knowing more about what router brand AND model, and knowing which ISP you are using would help us to offer advice.