I had just joined WikITree when this question was asked and missed it, probably because I was too busy doing my tree. Anyway, the website of National Records of Scotland has some info from the file titled "Robert Burns (poet): curatory and judicial factory papers relating to family" dated 1798-1801 and containing "Accounts of charge and discharge between William Thomson of Moat, writer, Dumfries, factor loco tutoris for the children of the deceased Robert Burns, for the periods May 1798 to May 1799, May 1799 to May 1800, and May 1800 to May 1801; and state of funds under the management of William Thomson, 1798-1801". You can see that on two occasions (1799 and 1800) she used the name Jean Burns. On another, she was described as Robert's spouse, and just five children were named as being young enough to still need a tutor (1800); what does that mean for eldest daughter, Elizabeth, who was not quite 15 when that document was drawn up? The document extracts are:
1) Copy minutes of meetings of the trustees of the family of the deceased Robert Burns (Dr William Maxwell, John Syme Esq, John McMurdo Esq and Gilbert Burns, brother of Robert Burns), 2 December 1797-17 April 1799 (endorsed No.1) (2 copies);
2) State of cash paid for the support of the family, docqueted by Jean Armour as Jean Burns, to 10 May 1799 (endorsed No.2) (2 copies);
3) Account of incidental expenses in the management of the affairs of the family, to 10 May 1799 (endorsed No.3) (2 copies);
4) State of Gilbert Burns' acceptance to Robert Burns' estate, with the deductions stated by the acceptor, from 1793-1798 (endorsed No. 4) (2 copies).
Accounts for period May 1799 - May 1800 including:
1) Copy minutes of meetings of the trustees of the family of the deceased Robert Burns, 1 December 1799; 22 March & 19 April 1800 (2 copies);
2) State of cash paid for the support of the family, docqueted by Jean Armour as Jean Burns, to 10 May 1800 (2 copies);
3) Account of incidental expenses in the management of the affairs of the family, to 10 May 1800 (2 copies).
Accounts for period May 1800 - May 1801 (2 sets) including:
1) Account of incidental expenses in the management of the affairs of the family, to May 1801;
2) Copy minute of the meeting of the trustees for the family (Patrick Miller Esq, of Dalswinton, Dr [William] Maxwell, John Syme Esq, William Thomson, factor loco tutoris and Gilbert Burns), 5 September 1800;
3) Copy indenture for the sale and publication of the posthumous and other works of the late Robert Burns, made between Dr William Maxwell, physician, Dumfries, John McMurdo Esq of Hardriggs and John Syme Esq, collector of Stamp Duties at Dumfries, acting trustees for the family, Gilbert Burns, farmer at Mossgiel, only brother and nearest male heir to the surviving infant children, and William Thomson of Moat, writer in Dumfries, factor loco tutoris for the children of the deceased Robert Burns and Jean Armour, his spouse (viz. Robert, Frances Wallace, William Nicol James and Maxwell Burns), and Thomas Cadell, younger and William Davies of the City of Westminster, booksellers, 25 February 1800;
4) Copies of letter from William Thomson, as factor, to the magistrates of Ayr, with reply, 9 & 14 October 1800;
5) Trustees account with Dr Currie of Liverpool, 1800;
6) Copy statement of cash paid for the support of the family of Robert Burns, from 10 May 1800 to 4 May 1801.
Copy letters from P Laurie, London to John Syme Esq, Dumfries, concerning the purchase and value of stock made on behalf of the family of Robert Burns, 21 June 1797 & 14 Feb 1798, referred to in the statement as given up to the court by William Thomson as factor loco tutoris, 10 May 1798.
State of the funds under the management of William Thomson of Moat, writer [solicitor], Dumfries, as factor loco tutoris for the children of the deceased Robert Burns, 10 May 1798; lodged 9 June 1798 (2 copies).
State of intromissions by William Thomson of Moat, from 10 May 1798 to 10 May 1799."
To see the document extracts, go to http://catalogue.nrscotland.gov.uk/nrsonlinecatalogue/search.aspx and enter CS97/101/15 in the Reference field to do your search.