Hi Katie. Oh my goodness you sound as if you are under a lot of pressure. When you are sleep deprived, have had a newborn and have mental health issues ten it is very hard to think straightvandcto take decisive action. People who have been unkind to you are probably not really mean but are ignorant regarding your mental health.
I think you should get a night nanny who will help you settle bubs into a routine. She would mean you could sleep every night, something which you need. Maybe just get your mum to pick up daughter from school but not stay so long. Everyone seems shocked at all the help you are getting but sometimes having people in the house can be quite stressful .
I think it is very difficult for you to take action. Some posters have been getting frustrated by this but again, this is because they don't fully understand your difficulties. So maybe get your husband or mother to set everything up for you . It is too hard sometimes to sort things out when we are so low physically and mentally.
You obviously care v much about your children and are being sensible by real using that you do need help.
Please ask either your mum or husband to sort stuff out for you in terms of help. Then concentrate on your sleep, cuddling bubs and spending a little btw of time with daughter.
Sending you a very firm hug and wishing you all the best. When times are v difficult remember ,'this too shall pass'.