No, you should not put “stay-at-home mum” on your CV (also commonly called a 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 could be left on your CV, but generally it is not relevant.
You should explain the gap in your CV in your cover letter if you feel it should be addressed.