The usual term in Scotland for "probate" is "Confirmation". You will still need to obtain a grant whether there is a will or not - a grant confirms the named executor's authority to act.
I am slightly concerned that your mother lived in Scotland (and presumably her property is there) but the solicitor is talking about Probate. That is associated with England rather than Scotland, but in either case, you will still need a Grant.
In England you can certainly do it yourself without seeing a solicitor. You collect all the paperwork and complete the Inland Revenue forms (paying any IHT beforehand if the estate is taxable). You then attend an interview at the Probate Registry which leads to the Grant.
Perhaps a Scottish law bod can advise on the procedure for Confirmation.