Is it my LHS transmission fluid?
 

just purchased a 99 Chrysler LHS from the original owner. The car looked to be in great condition, and it only has 70k miles. The car was driven by an elderly lady who increasingly put less & less miles on it. For example, the oil had last been changed in 2010 but that was only about 1,000 miles ago (first thing I did was change that). It had new tires put on in 2011 but that was about 100 miles ago. I drove the car about 200 miles yesterday (was a long way from home) & it drove beautifully. I drove the car to work this morning & first stopped at the store.

After getting back in, I shifted it into drive but I could see on the dash that the car didn't actually shift into drive. So I put it back in park & then put it into drive & all was well. But then when I got on the onramp & accelerated, the car sort of stalled & the speed/rpm was decreasing, but then it spiked & acclerated again & then it did that all one more time. It drove 10 miles to my work just fine after that.
The car is a little hard to shift into reverse from park, could it be just the transmission fluid even though it only has 70k? The fluid doesn't look bad, pink-brown color. I accidentally put in premium when the manufacturer suggests mid-grade--could that cause this sort of issue (I know, that sounds unlikely).

Any advice or helpful information is appreciated, thank you!