According to the calorie calculator on the Mayo Clinic website, at 5’4″ and 125 lbs (the weight you’d prefer to be), you would need between 1800 and 2000 calories per day to maintain that weight, assuming you’re fairly active (your job sounds like it’s pretty physical, plus you take care of a child and a house). So…5 tbsp of coconut oil is 600 calories, leaving you with another 1200-1400 calories to eat per day, which is a whole lot of veggies. I wouldn’t worry too much about gaining weight, unless you start eating a couple of loaves of coconut bread per day. Chances are, no matter what you do, you’re going to lose weight for a while on the diet, and eventually level off again.
I don’t have any information about hydrogen peroxide, though, sorry.