No, you should not put “stay-at-home mum” on your resume. Or any other fancy phrases that mean the same thing such as “home engineer” or “homemaker” or “family CEO”.
If you are applying for a job where your parenting and homemaking skills are directly transferable, like those in childcare, your experience as a stay-at-home mum should be left off your resume.
You should explain the gap in your resume in your cover letter if you feel it should be addressed.