My router perfectly captures the wifi. However, when I try to add a hotspot (Mode: Access Point), wifi (Mode: Client) goes wireless is not associated.
See the picture below for more clarification.
Btw, the I did the same producers on another router, and it worked fine.
I am not an expert on the Broadcom wireless, but it looks like you've got a BCM43217 and I believe that it can only be used as an AP or as a STA at any given time.
You might also want to read the following for some further diagnostics with "recent" Broadcom chips.
Edit: Another possible cause is that, if it supports both simultaneously, they need to be on the same channel.