Hello again Anne, (just sent you a PM too).
Not sure of that IGI record was a submission. The hassle is there IS a couple out there called John Braidwood and Jean Millar....I have seen their descendants trees online. My one is more elusive it seems

I found the following 1891 census on Scotlands People for Peter Rae (jnr) and his family in Larbert, as follows: Munro Street, Larbert
Peter RAE, age 39, Head, Foundry Warehouseman, born Larbert
Isabella RAE, age 40, wife, born Falkirk
Maggie RAE, age 17, dau, Toy Shop Assistant, born Falkirk
Peter RAE, age 16, son, Bakers Apprentice, born Falkirk
Janet RAE, age 13, dau, Scholar, born Larbert
Isabella RAE, age 10, dau, Scholar, born Larbert
Jane RAE, age 6, dau, Scholar, born Larbert
John S RAE, age 3, son, born Larbert
James B RAE, 4 mnths, son, born Larbert
I suspect that John S Rae has the middle name SCOTT after his mothers maiden name and brother James B Rae has the middle name of BRAIDWOOD after his father's mothers maiden name. Pure guess, but an educated one

Interestingly they are living next door to some Braidwood's but none that seem to match my family sadly.
Hopefully someone can help fill some more gaps for these families now....
Cheers Janine