40+ year Richmond native here. Here are some ideas.
As others have said if you are going to Tredegar, definitely go to Hollywood. They are a 5 minute drive or so between each other. If you do find some time to hit a battlefield, i would go to Gaines Mill or Cold Harbor, those 2 are basically right next to each other. The Gaines Mill walking tour is fairly short but its my favorite in the area. If you're going to stay in downtown Richmond and not do a battlefield, I would go to the White House of the Confederacy and walk around the grounds of the State Capital. All 4 of these sites are in a 5 mile radius. Just pay attention to street signs in downtown Richmond, many of the streets are one way. When you visit Tredegar, walk across the street and onto the Potterfield bridge. Potterfield is the pedestrian bridge that spans the James. It is an amazing experience and view. There is also some interpretive markers on the bridge, as well as Brown's Island, which you cross between Tredegar and the bridge.
Driving from Fredericksburg to Richmond, you go right by Guinea Station where Stonewall died. It's very close to the interstate and you can be in and out of there in less than 30 minutes if you like.
Fredericksburg I would hit Chancellorsville and the Wilderness before the actual Fredericksburg battle. More of the battlefields are preserved and they are right next to each other. They both have driving tours with many stops and of course many hiking trails. Both of these do have a lot of road noise from traffic. If you want the most serene battlefield in that area...that is Spotsylvania. Less traffic there. Hit them 1st thing in the morning and you would still have time to see the VC in Fredericksburg. Chancellorsville has a small VC as well.
I also highly recommend you download teh phone apps that the CWT has for these battlefields when you go.
You can send me a DM if you like with more questions