My mobile menu does not open at all.
Please share a link to your site, so I can have a look. Does it happen from the first time? Or just a sudden after certain circumtance. Probably there’s script conflict with one of your active plugins. Try disabling all of them (except recommended ones as mentioned here) temporarily. Once you get the menu opens again, to narrow down the source of the issue, re-enable plugins one by one and re-run your test in a row.
Here is a link: ModernDayMomLife.com
It’s done it since I started using the theme.
Also, I have deactivated all plugins and reactivated one by one and still does not work
Try flushing your site’s cache enabled with W3 Total Cache plugin. See if it helps.