Self employed and getting a part time job

I'm guessing you have your self-employed work on your CV? So they would know that's what you do/will be doing. I would just be honest with them and say that you would be dedicated to putting their job first?

I too am self employed, although work full time hours in a studio, but there are other self employed artists who are also doing other stuff alongside, one guy teaches at uni, and gigs, and works for the studio I'm at, unlikely it's the same sort of work you are doing, but as long as he gets the work done, they don't really care what he does with the rest of his time!