If the OP's ex, the OP's children and the OP all give credible evidence to the effect that *all* post addressed to the OP was handed to her, and that there was no NIP or reminder received, then she will be able to rebut the presumption of service.
The speeding charge is of no relevance unless she opts to do a deal. Similarly the evidence or lack thereof is irrelevant either way. Either the OP does the deal, in which case no evidence is needed of the speeding offence, or she defends the s. 172, in which case the speeding charge will go nowhere because they have no evidence that she was the driver.
Meanwhile, back in the real world, the OP moved house without updating the address on the V5C, and [claims that she] didn't receive the NIP. The court are somewhat unlikely to accept that it must have been lost in the post en-route to the previous address, rather than either lost after being served (delivered to the last known address), or not lost at all.
The choice is either to defend the s. 172 charge, or do the deal and take the hit for the speeding.