This type of art and name painting on bags, shirts, etc. are common in small shops in New Jersey. I would guess she got them done at a local shop or person in her town or at the Jersey shore (which the photo was taken at). I have shirts, bags and boxes with my name and character painted on from my childhood. I couldn't tell you of specific shop names as they were bought from my mother. I suggest Googling terms like "painted bags new jersey" to see if any shops pop up. They are very cute and something you and your baby will have for years to come!:)
I could swear I saw that ID'd somewhere on the forum and for the life of me can't remember. Try searching Melissa Gorga on the forum. It may have been in the RHONJ thread in "television & cinema).
Or, check her and Tracey DiMarco's twitter (a reality star on Jerseylicious) bc she carries it too. Tracey will tweet her fans back a lot especially when they ask for an ID on a product she was
Given for free to promote (which I believe this was).