Money

[getyaminkehout]

To ask for the child benefit money..

I do work but only one day a week, partner works full time and has done for 10+ years. I'm just feeling low as any problems I seem to have all stem from having little to no money.

Like others there's not enough information, OP had used emotive language like 'allow' which prompts a certain response from other posters.
It seems each month OP has £240 and pays for fuel , trips out with DD and personal things, get DP had £300 but it is that saves for their daughter, pays for her clothes and pays for his own personal things, it's fair to assume he also pays for his commute/travel when OP isn't giving him a lift. I'm not sure this is actually unfair, depending how much he's saving for the child he could actually be left with less than OP , it's definitely less fun buying clothes for your child than it is spending your money having nice days out with them.

OP there's lots you need to clarify before anyone can actually make a judgement

child benefit is supposed to be paid to the main carer of the child as it also forms a legal record towards your national insurance credits for your state pension. These credits are only made to the main carer and only provided you are not working enough to pay income tax. They are paid until a child is 12 if i remember rightly. You can request direct with the child benefit office to have it changed to your name and paid into an account you can access.