Vibration in right front wheel worse when going around a curve to the left

Most Good garages can do these for you for free or a small cost.
The things to get checked are...
First get all your wheel bearings checked. Especially the front ones. A worn wheel bearing will give a thrumming noise when driving which gets worse when you turn corners.
Next have ALL of your wheels checked to see that they are balanced correctly and ALL of your tyres are in good legal condition. Out of balance wheels and worn out tyres can cause vibrations at certain speeds.
Have all the suspension mounting points and rubbers checked. Worn joints move too much as you drive also causing vibration and noises.

Are you sure the lug nuts aren't loose?

sounds like you have a bad wheel bearing, does sound change going around curves ?

I would suspect deformed tyres ,they do go out of round with age and the sun which does wonderfull to tyres

check and test hubs and c/v axles

Has to be a front axle(inner joint) Very common. Will be able to feel the play with the wheels off the ground.

Are you getting a humming or grinding noise with it as well? This may be a wheel bearing issue causing the vibration which will be worse under accleration.

Replace the right front wheel bearing

Have the tire checked to see if it is out of round,maybe move it to the right rear to see if it changes,also,have the front end alignment checked.

You could have a bad wheel bearing or out of balance front tire. Without the trailer if you go on a curve the outside tire spins slightly faster than the inside. If you notice more vibration going left, then the right tire is the outside tire.