Power reserved just means the other executor(s) carry out probate without the power reserveds signature. The OPs wife has not done anything wrong. If her brother is not happy, he can apply for double probate meaning both will have to prove the Will. As for using researchers to find another Will, it sounds like he clutching at straws. The MIL solicitor has provided the last known Will and all he needs to do is check if there's another one lodged at the probate registry, this is an easy task. If I was the OPs wife I would ask the PR myself and ask the solicitor to provide written confirmation t

If its signed fir you can track that it has been received, simple proof of posting is just that, proof that you sent it, not that they received it. Persinally i would use signed for for this