parental rights for daughter 6yo

Hi, was wondering if i can get some advice.

I very recently caught my partner cheating by sending videos and chatting to another guy and now we intend to separate.
We have a daughter together who we both now love dearly. When she was born my partner decided to take all of her maternity leave and it suited us as i was working self employed and had a certain flexibility to help her out.We had lived together for 6 years at my fathers house until we found we were pregnant and moved to our own house.
In our new house our landlord only needed 1 signature for the lease so we agreed that she would put down her name as the self employment was a bit hit and miss.
After her maternity was about to finish she decided that she would like to go back to work as she was having a hard time with our daughter.I agreed and thought it would be good for her so i gave up my own job that was becoming less viable anyway.
As i was to become the stay at home dad we decided to put the child benefit in my name as i was to be her primary carer.
My partner works in care so she works different 6hr shifts 5 times a week.
I found it very difficuilt to find something suitable for work as from age 3 to 5 she was only 3hrs a day at nursery plus my partners shift patterns and it wasnt much easier as she went to primary school she just did not like to be away from us so child care was out the question.
In the past year I have made a huge effort trying to find something suitable but now my partner is saying i have not been trying enough and wishes to separate.
She has been telling everybody she could that i have been lazy, doing nothing in the house and not looking for work which is just simply not true.Even saying so to my 2 sisters who have now fallen out with me as they have got close to her.Said i was only there to spend her money and i was not buying anything for my daughter yet i gave up 5 years and my job so she can go back herself.
We are still in the family home but she has asked me to leave her and my daughter but am reluctant to do as i still love them both.

If I am forced to leave what would be my parental rights,should i give her back the child benefit or will that affect my rights if things get messy. Also as the house is only in her name can she force me out away from my child?

sorry for the long winded post but any help is very much appreciated John

All I can suggest is :-

1. DO NOT leave the matrimonial home until child arrangements are agreed and signed .

2. DO NOT transfer the child benifit into her name as this will also weaken your position.

We are not married so i think that is where i may have a problem

Sorry I missed that. Ok as her name is solely on the lease I believe this could give her the right to ask you to leave. Someone else could confirm this.

With regards to child benefit I would make sure that remains in your name for the time being.