I do not think it is possible to have stops on a route show in the side bar.
If you have your stops pre-planned at home, a work around using MyDrive would be to send them to the device as a destination and then rename them in My Places on the device as 01, 02, 03, etc.
This will show them on the device in numerical order. Give them a significant name after the number so that you remember what it was.
Another way would be to save the place files on your computer in folders like East, South, Rockies, etc., each with the .ov2 extension. Now import them with MyDrive Web and synchronise them with your 510.
They will be shown in My Places, at the bottom, in alphabetical order, below your regular named My Places.
They do NOT display the .ov2 extension there.
The list of all POIs in a folder will be displayed in distance from current location under Search.
At Settings > Appearance > tap "Show POI lists on map"
It will now show all your lists with the attribute Hide.
Tap on hide of one of them and select one of the 5 preset icons for that folder.
To see them like your favourites you must restart the device.
I suggest you test that with a few location locally so you can check how it displays places by distance.
Please do not hesitate to ask additional questions or ask for clarification.