A.C.
If they ask about your current work situation, tell them the truth......
1. you were offered a full time position and accepted the offer
2. you quit your part time job
3. let them know that you would consider accepting a position at their company if offered
4. you can say that you do like your current full time position, but your career development would have more potential if you accepted a postiion with their company
Use the fact that you received another offer as a positive. You are wanted and valuable. They (the 2nd full time job) have a very small window to make a decision to have you work for their company. They need to act fast. You are the one in control! They need to "woo" you to work for their company!
Let us know what happened.....Take care, A.