Any advice on getting a part time job as a J2 without mentioning you have a J1?

I am interviewing with a company where my J2 will be part time (I know its not really in the spirit of what a lot of you do) but I really like the assignment and the domain. However, they keep pressing me on the fact that its a part time and is that okay? does that work for me? How does that work for me when the pay is good but part time?

I have made all the mistakes before saying by saying that I have another job (claimed it was part time) but this would by my primary, that "at this point for personal reasons...." nope they saw (falsely) 'single mother no child care' waiving as a big red flag, I tried to imply that circumstantailly I was just rich and didnt need to work full time that got awkward. It did seemed to go well but I think I just got plain beat out for the position.

What is a good excuse to want part-time?