Is this plan too much to lose weight?

Hello,

I workout 4x a week (Monday-Thurs) with a trainer. I've gained muscle. I am not losing fat because I havent done cardio.

Last summer, I was working with my old trainer 3x a week(MWF) & running 2x a week(TuThurs). Now, I work out 4x a week with this new trainer. (M-Th).

I want to be able to lose fat. I would run/walk 4 miles. 2 miles to my desination and 2 miles back. I want to do this again along with healthy eating.

What should I do as far as cardio and how many times a week? I want to do it in the mornings. I was actually thinking that I can run in the mornings everyday then go to my trainer in the evenings, but then it might seem too much and I would overwork my body, so Should I run 2x a week? like Monday and Fridays? or 3x a week, like Tuesdays thursdays and Saturdays?

Give me an idea of what can help! Thanks!