Who is the Executor of the estate OP? If the deceased person wrote a Will, it is highly likely that they also appointed an executor to handle their financial affairs when they die. That is who will be in charge of what goes on.
If it is a solicitor, you are pretty much stuck with him and his fees, both to administer the estate, and sell the house and disperse the sale proceeds to the beneficiaries. You could ask him to waive his responsibilities as Executor, but why should he? It's how he earns his living after all.
If the Executor is one of the 3 kids, or another person, no they do not need to hire a solicitor to carry out Probate on the estate. They will need a solicitor to handle the sale of the house, but everything else the executor can do themselves if they are willing to put in the time and effort to do so.
Who gets to do what all depends on what the Will says re Executorship of the estate.