No need to be sorry zana, you are brave for admitting how you feel.
I have a firm theory that things happen for a reason and every cloud has a sliver lining. I asked for part time and was refused (teaching as well, where pt roles are very common and easily accommodated) and it was what prompted me to give up work. Without doubt the best choice I could have made. I am sure everything will work out for you 
Consider the value you give to your family that is not money. Your salary is only a tiny fraction of what you can give the household. All the other ways you "contribute" (in a none monetary way) become more important when you are at home. Socialising with your children, getting involved in the community, being consistent in approaches to behaviour and routine, attending school events and extra curricular activities. Just the security and consistency of always being there.
Because I am not knackered or stressed it has a hugely calming effect on everyone else (husband and children), making everyone else feel less harassed and rushed. Without wishing to sound like a 50s housewife, is has been very good for my marriage that DH comes home to a smile and a calm house, where everyone has done their homework and dinner is ready.
It wasn't like that when I was working, personally for me I couldn't cope too. I was too busy, too stressed, too exhausted to cope with two toddlers. So I definitely don't think you are anything like pathetic Zana. You are brave for taking the decision to do something different and give another option a try 