To OP
Even if you don't want to use a solicitor for the Grant of Administration to your late father's estate, it would be worth checking with someone how the two properties were held- as in, was your mother on the title to either or both and if yes, as Joint Tenant or Tenant in Common.
I find with older people, very often the widow was not on the title which is why the Grant is required. If your mother is on the title as a Joint Tenant of either or both properties, then the property(ies) fall outside the estate of the deceased and do not need a Grant.
Your mother should make a will now if she wants to benefit any one of the children over the others- if she does not make a will, her estate will be divided equally between her surviving children.
A Will speaks from date of death so, assuming your father's estate is resolved before her death , that will make life easier.
It would be possible for the owners of the outstanding one third share - if applicable- all to disclaim so that everything goes to your mother.
I can see a right bag of cats developing if your mother dies leaving her share to one child only while the others hold onto their share of the one third share.
I've had my fair share of disgruntled offspring making life very difficult for other siblings.
mf