Solicitor
This is a perfect example of a common failing in the legal profession (and indeed in many other professions). The failing is in lack of clear communication at the outset and failure to properly manage client expectations. However, in the administration of an estate, the correct position (in my view) is as follows:
1. The administrator of the estate (in this case your brother) is the client.
2. The solicitor has a duty to all beneficiaries, but he takes instruction only from his client.
3.If at all feasible, the solicitor should arrange matters so that the administrator is the conduit for all communications. The good sense of this becomes obvious when you have a large number of beneficiaries.
I rather imagine that if this had been agreed at the outset, you would have had no difficulty accepting the situation. Instead, you now feel hard done by: the real problem is poor communication at the outset. The solicitor, incidentally, is probably saying to himself "that's what I get for trying to do a bit extra and be helpful to that guy". I know, I've done it myself.
As a beneficiary, you are not liable for the costs of administration. The administrator is liable for the costs. Of course, they must come out of the estate assets and this therefore means that for practical purposes the burden will be shared equally by the six children.
You say that
"Since he was writing to me and taking instructions from me would that not then make me a client anyway?"
Certainly it might; but you are not the administrator of the estate; if you are nevertheless a client, that might entitle the solicitor to invoice you and this would be separate to any bill sent to the administrator; so I wouldn't go down that road.
The real problem here is in not making things clear from day 1. (I am assuming that things were not in fact made clear; But it is possible that the solicitor wrote to each family member and made it clear that he had been retained by and was acting upon the instruction of your brother, but that you simply failed to understand this). A mistake certainly, but in fairness not a hanging offence. Both you and the solicitor will undoubtedly have learned from this.