I am unable to comment on what another Solicitor may have said to you as I was not privy to the conversation.
1. With respect to the sister applying: Where minors are involved, a parent may apply for letters of administration (LA). Alternatively, a statutory guardian, or any guardian appointed by a court can apply for letters of administration. As such, an application could be made for the sister to be appointed as a guardian for these purposes and apply for letters of administration on the minors behalf. ( see para 32 of the below attachment)
2. Two parents applying for LA: Where two persons are entitled to LA in the same degree, if it cannot be agreed that one person applies for LA, then a special application would have to be made to the court for two persons to be so appointed. I do not believe this is necessary and would be a time consuming and expensive task. Ordinarily one person would be appointed and that person would act in the best interest of the beneficiaries to the estate. ( see para 27 of the below attached link)
3. Possession in the house that is held as joint tenants would pass automatically to the surviving tenant. If they were owned solely by him, then you may speak to this person to be allowed access to them. If they refuse, then you would have to go court for an order allowing you access. The difficulty you will find here is that you would have to be able to identify what it is that you are claiming an entitlement to. So, for example, if you are saying he has tools there you would have to be able to identify what tools specifically and that he is the owner of those tools. You cannot demand that she lets you in, you would have to have an order from the court specifically allowing you access.