Engine feels like it wants to stall backing trailer up slight incline

What is your question?

Help! I have a 2009 Ford F-150 XLT V8 6-speed Auto. I pull an 8x10 trailer with lawn equipment on it about 4-5 days a week. I park my trailer at my brothers house when I’m done. It has a slight incline. When I go to back up into the driveway off the street, the engine seems to want to die. Most of the time, I’ll quickly put it in neutral and rev the engine to “clear it out”. Yesterday, I let it go to see what it would do. It cleared itself out without me putting it in neutral or Revving the engine. It seems to happen mostly after a long drive when it’s warm out. We backed up several times to see if we could see any obvious causes. My brother said the engine shook and the fan belt got real slow. He could see the white lettering on the belt (he could see it. He couldn’t read it lol). Spark plugs and coils were changed 2 weeks ago. Any suggestions? Thanks in advance.

What makes this problem better or worse?

Hot weather up slight incline

How long has your 2009 Ford F-150 had this problem?

Several months