Hi, Nokaze.
"If I was your mom..."-is the 2nd Conditional, you are right that "were" in such setnences is used more frequestly, though, "was" is also correct as an option
--But you're not, though.-"though" here is used for emphasis with no specific meaning of its own just to highlight the disagreement expressed with "but" (can only be used like this in a colloquial speech)
Though can also be used after adding a fact, opinion, or question which seems surprising after what you have just said, or which makes what you have just said seem less true.
Examples:
I think she's Swiss. I'm not sure though.
Two heart attacks in a year. It hasn’t stopped him smoking, though.
Hope that'll help))