Basement stool issue

We have a basement bathroom. If you flush the stool once, with or without a "load", it seems to flush normal. If you flush it again, soon after, it doesn't flush well. It doesn't swirl. If you wait a couple of minutes it will flush again. It will swirl.
If someone puts a "very heavy load" in the stool it will back up and take several flushes over a period of hours in order to clear it out. A normal load won't do that, but it will slow down and not swirl for several minutes afterwards.
I'm thinking of either trying to clean the line myself with a rented auger, or hiring someone to do it. I've seen people augering lines with the toilet in place. Would this work? Or should I have a professional come in and remove the stool and have the line augered with a high powered device?
It has been in this condition for at least a year. Thanks in advance.

 

Probably best off removing the toilet and having the line snaked.
This will confirm that everything is clear in the pipe.
There is a chance that the plumbing is bootleged (and not done properly) and does not have a proper vent.

 

Yes. That's what I was thinking. Have the toilet removed and the line snaked.
How do I know if it's properly vented?
Seems like it's always been slow on the second flush. If you wait five to ten minutes the second flush works fine.

 

A good sewer camera down into the drain will allow evaluation.
The best camera will be a self-righting type that keeps up and down properly viewed.