why I can’t do redirect for homepage.

Your site appears to be cached using Cloudflare. You will need to clear any caches.

Does my issue in my wp-admin cause due CloudFlare ?

How can CloudFlare be bound with my admin panel ?

What is your issue in wp-admin?

The redirect checker uses an external service to check a URL. If your site is cached using Cloudflare then it will affect everything, including the redirect checker.

I have cleared https://www.plumberwoodlandhillsca.com and https://www.woodenplumber.com

Take a look at this screenshot:
https://yadi.sk/i/qF34vvTJ8wgSBA

The issue is remained

Only Homepage to Homepage between domain this issue

Redirects for other pages are without issues

Sure. Your site also appears to be using other caching software. Anything that is cached will need to be cleared otherwise the cached version will be used.

Thanks. Now it works.

When homepage redirect was not working – Google Bot could not be redirected too?

I couldn’t say, but if your cache was returning a page then it would be the same for everyone.