I just need to keep very quiet and tip toe for a while
Absolutely! And since your mum apparently is supportive she's a perfect repository for any new-found information and paperwork. Use her address and phone number if you need to.
Your first visit needs to be with a solicitor. Think a bit and write your questions down before-hand. Take your mum with you or someone to act as a 'second set' of ears and/or to take notes. I did this for my BFF when she saw her lawyer for the first time. There was so much to remember that two heads were needed to be sure things were remembered correctly.
Things to ask about;
The issues surrounding the house (staying, selling, buy out, masher order, equity division)
How to establish grounds for divorce
Equitable division of other assets
As far as renting, remember that you could probably make do with a 1-bedroom place to start with. Either you and DD could share or you could try to get a sofa-bed for the living room. A friend lives in a very expensive area and when she was contemplating splitting from her 'd'H, she determined that she and her then 11 year old daughter would have to 'make do' that way as she couldn't afford 2 bedrooms.
Also, do consider moving near your parents. Not right away perhaps, but consider the cost of living where they are vs where you are and whether you could find a similar paying job there. As far as DD's school, well, children have to change schools and move for various reasons all the time and they adjust.