Sounds to me like you may be dealing with a transaxle problem (Transmission).
Your vehicle is equipped with a 4F27E Transmission. (4 speed, FWD, 270lbsft max torque, Electronic Control). This assembly operates much like many many other Automatic transmissions equipped on vehicles for decades.
It uses a torque converter to transfer engine torque to wheel torque and engages its gearing using clutch sets and fluid solenoids. Many different things can go wrong with an automatic transmission but the first step in diagnosing issues that show symptoms of it being transmission related, is always to check the fluid level.
To do this properly, you'll need to: drive your vehicle through a range of speeds, for around 10 - 15 minutes (i.e. a trip to work, or a trip to the store and back). Then, after driving and placing the selector in park, With the engine still running and parking brake set, remove the transmission dipstick, and wipe it clean. Reinsert the Level stick, and wait 5 seconds. Remove the stick, and inspect the end of it. You should have 2 markings, and possibly a "Hash Marked" area between them. If the fluid level is within the hash marks, no further than the top mark, and no lower than the lower mark, then your level is ok.
If you don't have a reading on the stick, add 0.25qt of Mercon LV Transmission Fluid at a time through the stick tube using either a funnel or the stick itself, allowing 10 seconds between each pour before checking the level. Repeat as necessary until the fluid is at it's filled marking.
Also, this may sound funny, but you can tell a lot from transmission fluid by its smell as well. If it smells sort of "Bland" and a little bit funny almost like plastic, you are ok. But, if the fluid smells like it's burnt, then you may have an issue internally. Ultimately, I think your issue lies within the drivetrain, more than likely transmission related. But this is the first step of inspections performed by professionals like myself when working in the field. Hope this helps.