Having Troubles Getting The Weight Off

One week is not enough time to see progress. Have you been logging you food intake accurately during that week?

Exercise is not necessary at all for weight loss (although good for health). Breastfeeding will naturally create a deficit (size of which depends on how much milk you're producing), set yourself to Maintenance and log accurately, food scale would be the most accurate way of determining food intake.

IF 16:8 is only useful if it works for you, it's just a way to manage your calorie intake (i.e. by skipping breakfast you have more calories available for lunch/dinner).

Weight naturally fluctuates constantly, this is a combination of food/waste in the system, regulation of fluid in your body in response to things like hormones, sodium, carbs, alcohol, dehydration, etc.

A pound of body fat is approximately equivalent to 3500 calories, to gain 4lbs of fat you would have had to have eaten at maintenance all week and then an additional 14000 calories somewhere. I'd say it's pretty unlikely that happened?

Weight loss takes patience and consistency.

I'm sorry you are feeling frustrated. Take your time and do what works for you. Exercising isn't vital to lose weight although it is good for your health. Losing weight is more about how many calories you are eating no matter when you eat them. Keep track of your calories and if you feel like taking the kids to the park you can get a little exercise in by walking there. If not then you just burn a few less calories that day. So many folks think that they can't lose because they can't exercise. That is totally untrue. Exercise is good for you definately and I find it is a great appetite suppresor for me but all I've ever done is walk and I lost 100 lbs. Hang in there and don't give up.