You will have so much to choose from, you will wish you had a longer stay! Also, your two locations may seem close, but will be slow traveling.
It is a lovely drive from the busy city of Trier along the Mosel, and the road crosses back and forth across the river through many pretty little villages you'll wish you had time to explore.
I think you're okay with driving yourself, as the tasting rooms provide small samples and are careful to give you bread with the wine (no tasting on an empty stomach!). Sweet wines do go down easy, just don't stop TOO often!
One of our favorite vintners is the young family who own Weingut Bollig (Doris and Wolfgang), just a short way up the river from Trier in Trittenheim, so it would be a good first stop. They are very hospitable and have GREAT wines. They speak excellent English and enjoy showing off their vineyards and their wines. You might want to get a couple of bottles to savor in your room in Beilstein!
Next you will go through Piesport, home of the famous "Goldtropfchen" riesling--will certainly want to do some tasting there!
Bernkastel-Kues has a medieval town square full of half-timbered houses around a center fountain, the "Pointed" House" built in the 1400s, and the also famous Bernkasteler-Doktor vineyard wines. If you have time, do go into the town and wander a bit; I think you'll find it as charming as (and perhaps less touristy) than Cochem.
Traben-Trarbach, Briedel, Zell (with its picturesque pink palace and "Black Cat" rieslings), Alf-Bullay and Ediger-Eller are all other riverside villages where we've gotten good wines, all before you reach Beilstein.
If you go north on the river road from Cochem later, perhaps to see the wonderful Burg Eltz, the village where you make the turn to go to the castle is Muden, and it has a great restaurant: the Hotel Sewenig is directly on the river and has an interesting history (river flood stages are painted on the side) as well as good wines to enjoy with lunch on your way back from the castle.
Have a wonderful time!!