Thanks for the additional information. As you know, there isn't much online for Scotland since the 1901 census (and that is only an extraction, not the images). Here is what I have found from the bits that are available.
In the 1901 census for the UK, here is the family listing for Registration Number 619, Registration district Tarbolton, civil parish Tarbolton, county Ayrshire, addressXXXXX:
Andrew McClelland 28 M
Maggie 24 F
Jessie 3 F
Charles 1 M
That puts Jessie's birth at around 1898 rather than 1900/1901. That also fits more in line with biology (i.e. the odds that a couple married in Nov 1897 would not have a first child within 3 years if they weren't infertile).
In the 1891 census, Andrew is listed as 19 unmarried working as a "farm servant" in the employ of Hugh and Christina Hunter and their family in Mossbog[sic], Ayrshire. In both 1891 and 1901 censuses Andrew is listed as having been born in Tarbolton.
Margaret "Maggie" Stewart is probably the daughter of John and XXXXX XXXXX. She is the only XXXXX XXXXX born about 1877 in Tarbolton. Here is the 1881 census:
XXXXX XXXXX 36 M Head, born Dull, Perthshire, occupation: ploughman
Elizabeth 30 F Wife, b Coylton, Ayrshire
James 7 M Son, b Tarbolton, Ayrshire
Elizabeth 5 F Dau b Tarbolton, Ayrshire
Maggie 4 F Dau b Tarbolton, Ayrshire
John 6 months M Son b Monckton, Ayrshire
XXXXX XXXXX 25 M Brother, b Dull, Perthshire, occupation: general labourer
Be sure to check out the historical and genealogical sites below:
Robert Burns was made a freemason in Tarbolton and helped form a debating club (The Bachelor's Club) there. This link has some interesting information and an imbedded link to a street map of Tarbolton.
I really envy your trip. Ayrshire is a beautiful part of Scotland. I haven't done much personal research in that part of the country, but we have vacationed there and at Newton Stewart in Wigtownshire. Mostly we have holidays in the north part of Scotland. I hope you are renting a car to make getting about a lot easier for you.