Choosing between two post-docs where one is with my PhD advisor
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.)