Yes, he will only have to pay maintenance for your 2 year old - spousal maintenance would only be if you had given up a career many years ago to raise a family with him and wouldn't be able to get a job of a similar standard due to having had too long out of work.
Regarding the house, it's unlikely you would have a claim on the property unless you can show that you have contributed financially to the purchase - did you pay any part of the deposit?
You can go to CAB for advice regarding benefit eligibility or look at www.entitledto.co.uk - you would probably be eligible for housing benefit on a 2 bed property, income support and child tax credits (and child benefit obviously). If you got a job of 16 hours or more a week you would also get working tax credits and 70% of your childcare costs paid for.
Any advice very gratefully received. I'm currently living with my partner of six years. I have one 8 year old from a previous relationship and one 2 year old with my current partner. unfortunately we are now splitting up after quite a few years of a very bad destructive relationship. My partner owns the house and we're not married so I just wondered what (if any) rights I have. Obviously he is only father to the youngest child but has been a father to my first child since he was 2. He is refusing to leave the house that we only just bought last summer. This is fair enough... it is his after all. I don't work and the 2 year old is not at nursery. I presume that my partner only has to pay child maintenance for his child and for nothing else. Does anyone have any advice on this messy situation?