If a woman was immunised against tb, would that immunity be passed on to her children?

No: The vaccine to protect against TB - BCG - is only partially effective. Many people who get the BCG also get tb. Any immunity affordind by the BCG is not transmitted in utero.

IMMUNITY TO TB: There is no vaccine to immunise against tb, and if you get TB and it is treated and cured, you are not able to pass any kind of immunity to your children.