Here is my work out schedule.

MT-Hike 3.5-4 miles (1000 ft elevations gain) I do this in 60-90 mins.
W-Rest
ThF-Walk/Jog 3-4 miles (jogging about 1-2 of the miles)
Sat-1 mile leisurly walk (I count this as rest)
Sun-Walk/Jog 5 miles (jogging about 2 of the miles)

Is 2 days of rest important or should I add a 6th day? I don't do any weight right now because I have to do the majority of my working out with a stroller and it's my only chance to work out. I was considering adding a 30 min balance ball work out 3 days a week, but that would mean I'm working 2xs a day sometimes. Does rest help with weight loss, or does is just to help your body recooperate?

For me it just depends on listening to my body for when it needs a rest. If I notice the quality of my runs suffering, then I know I need a rest day. If I'm not putting 100% into my workout because all I can think about is how tired I am, it's time for a rest day.

Personally I like to exercise 5 days a week .... seems to be enough to keep me from feeling burned out and I can take a rest day when I need to.

Rest days are more important, I think, when you are doing very high intensity or intense weight training... I usually take Friday and Saturday off, if it works that way, other weeks I will have a third rest day in there, or other weeks, less... Just listen to your body as FatPants said..

BTW Miss Fat Pants, you should really change your name, you are NOT fat anymore girl...

Rest days are as important as sleep. They give your body time to make repairs and it's those repairs that make your body stronger. Rest days do not mean that you have to vegetate on the couch though. Your leisurely walks are great and do not put any strain on your body or intefere with the repairs.

Sometimes I work out twice a day as well, especially if I want to do weights. Just listen to your body, it will let you know if you're doing too much.