Transmission clunks momentarily like it drops a gear. Car also dies unexpectedly when slowing down.

Our 1998 Park Avenue occasionally "clunks" like it is suddenly dropping to a lower gear. It does not happen all the time and seems to be worse after the engine is hot and we turn it off for a few minutes and then turn it on and start driving again. That is when it "clunks" the most. We just did two 600 hundred mile trips and didn't have any problem while on the highway. On the one trip, we turned the car off to wait for some road construction for about 10 minutes. When we started out again it clunked and lurched a couple of times and then we were fine for the rest of the trip. It has only happened when we are going at slow speeds, but has also happened twice while sitting at a stop light, while in drive with my foot on the brake.

I am thinking this is some kind of electrical problem rather than a transmission problem. The battery was old and I changed it because of winter coming on. After the new battery was installed, the car ran fine for 3 days before it acted up again. It had been acting up every day for a week or so before that.

Another problem to go along with this is that the car will sometimes die. I think it only happens when we are slowing down with a foot on the brake. The car just quits and we have to put it into neutral or park and start it again. The clunking and dieing problem seem to have started at the same time.

I don't know if it is related but 2 days ago the right turn signal and right headlight also quit working.

I appreciate any insights or direction you can give me.

Brad