Choosing between two post-docs where one is with my PhD advisor I am currently a post-doc researcher for two-months at a department (say A). I also graduated with my PhD from the same dept. The post-doc is not funded with any project but with department money and I am expected (pushed) to bring funding from industry partners as soon as possible. 

I recently got another post-doc offer where they already have project funding. The place is closer to my home, but I have heard some poor remarks about PI. The project is also well-aligned with my PhD work.  

My question/confusion is as follows: my PhD supervisor at department A, who works remotely, insists that I should not leave the current position. She is a great person and I loved working with her. I have also heard that it will not be good on my CV to switch post-doc so quickly (just after 2 months). 

Does anyone have experience regarding this? Is it really true that switching positions will look bad on CV? 

Many thanks everyone in advance.
Your primary goal during a post-doc is to improve your chances to land a permanent job in academia. You should compare both jobs with that goal in mind. Especially interesting is the recent track record of both PIs: How many top publications did they recently have? How many of their graduates have made it to permanent jobs? You should absolutely watch out for "red flags" that may make your life difficult, like (trustworthy) hints about a poor working environment. Based on your comment, there is a reason to be a bit skeptical, and you are well-advised to seek more information.

Generally, switching to a different place after your PhD is a good idea. You want to communicate the idea that you can do a good job in different environments and with different people. You also don't need to be concerned about switching after two months. It's quite typical that people do a few post-doc months at their PhD institution while looking for a job somewhere else. (If you're still worried, you don't even have to mention in your CV that the last two months were a post-doc; you can just specify the duration of the full employment at your home institution, and that did your PhD there.)