it is a really tough time, but well done for making the break. I felt so many emotions after splitting with ex; it will probably be a rollercoaster, but it will get better!
First things first - start by getting your financial duckies lined up - I don't know if you are married, if you have any assets etc., but book a free half an hour with a solicitor. Next, contact your local council and get your single occupiers discount for your council tax and see if you are entitled to any housing benefit or council tax benefit. Next call tax credits and put in a claim as single person. You will need your earnings for the last financial year and current childcare costs.
I find that the most difficult part of working and having children is keeping all of the balls in the air, managing school runs / childcare, especially if one / all of the children are ill. Have a chat with your boss and explain the situation; see if you can start doing flexi-time if you are not already, and explain that sometimes you may need to take unarranged time off - my employers are very understanding of my situation and I think it helped that I was honest and upfront about the change in my home circumstances from the off. Get a contingency plan in place for what to do if you need emergency childcare (family / friends / other school Mums) who can help out. I work flexi-time and do slightly shorter days to pick kids up form school, then work late on the day my ex has the kids to make my hours up. I have the phone numbers of 3 Mums who live close to the school in case of emergencies, and a very lovely childminder.
As to telling the kids - tell them Daddy has gone away for a few days, then I advise you to tell them all together with your ex, and keep it simple and as positive as possible. Young children just want to know that Mummy and Daddy still love them, and it is not their fault. Something along the lines of "Mummy and Daddy still love you, but are going to live in separate houses from now on. Just imagine, you get to have two bedrooms now!!!". That is very concise, but there are plenty of threads on here if you do a search about how to handle that really hard conversation well well.
Why do you have to tell the inlaws? Will your ex not tell them? As for your parents, I had exactly the same problem, they came around eventually, but it is horrible not feeling you have their support, so I do sympathise with you on that one. Just be honest with them and tell them how unhappy you have been and how you think your ex is having a negative impact on your dd.
You will be fine 
. Anyone in RL you can chat to today?