Crawler (eg. googlebot) go to wrong path. How to direct them going within our sites?

Hi I would like to receive some help from you all.
Our site : mangaarts.com.au/home and mangaarts.com.au/onlineshop are no longer listed in Google or any other search engines.
I investigated for this problem and found out that once crawler go into our sites (both), they go to wrong place!!!

Our site uses shared SSL, so our site actual path is :

https://s13.web-servers.com.au/~mangaart/home/
https://s13.web-servers.com.au/~mangaart/onlineshop/

However, once crawler comes in, they go to:

https://s13.web-servers.com.au/home/
https://s13.web-servers.com.au/onlineshop/

~mangaart is missing! (I found this in our admin section under "who's online".

If you know how to fix this, please reply this post.

With lots of thanks.

mangaarts

I would recommend on spending the extra $10-20 and get your own SSL. That would solve your problem and build more trust with your customers

Hi Thank you for your reply.
We are considering to get own SSL, however, this problem does not happen on other sites (shared SSL).

Our other sites are :
https://www.comicartgear.com.au/home
https://s13.web-servers.com.au/~mangaart/comicartgear.com.au/home/
and
https://www.copicfantasy.com.au/home
https://s13.web-servers.com.au/~mangaart/copicfantasy.com.au/home/

Crawlers go through these sites within our sites and indexed.

So I would like to know why this happened on mangaarts.com.au/home and mangaarts.com.au/onlineshop and how to fix them.

If anyone know HOW TO FIX much appreciated.

mangaarts