oh dear, you do sound down in the dumps. And in a depressive cycle, I think.
First off, start with the basics - are your DC fed, cleaned and loved on a daily basis? If so, then you are doing ok as a mum.
Second - housework is not the be all and end all of being a good mum. Do your DC go to any playschool/groups to give you time to yourself to get on with things? If not, have you heard of Homestart? It can be a godsend in situations like yours.
Third - start small. Set yourself (initially) one thing to do in a day; focus only on that one thing and ignore everything else. So, it could be folding washing one day - or if you have the Himalayan range of washing piles, then just focus on doing one pile at a time. Sometimes the magnitude of a task is too daunting in itself, so break it down into half hour slots - one pile shouldn't take longer than that.
Fourth - make sure you are getting enough sleep and proper food as deprivation in both of these areas can contrbute to low mood and depressive feelings
Fifth - try and find one thing to do outside the house a week - get someone to sit with your DC and GO OUT, even for just a couple of hours.
Your friend who dumped you might have just decided that you haven't moved on at all since your DH left you and therefore there is nothing more to say. Ignore her and the reason - sm he ay choose to stay friends anyway.
hear hear thumbwitch and bump Try setting yourself 15 minutes to do one task and then taking a break for 15-20 minutes then do another 15 minutes etc , you could choose another task if you get overwhelmed. Also check out some of the threads in good housekeeping. My house isn't great either, housework keeps. And what thumbwitch said