Should I tell my boss I am quit or let her decide on the good term?

I just accepted a part-time job (that pay higher with more benefits) beside my current full-time one. My current one is ok except I am underpaid and no benefits. As much as I want to keep my current one by reducing my hours, my part-time schedule is not consistent. I know I will have to leave the current one any time soon but wonder how I should approach this with my boss, especially when she knows about my part-time. Should I tell her I quit or show her the part- time schedule and see if she can work out on my schedule or let me leave? Thank you in advance for your inputs

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