How can I evict my brother?

Wow, that's a tough situation to be in. I don't see any chance of your bum of a brother getting another job and moving out - it seems as if his plan is to stay unemployed. It is really up to you to make him leave, and words alone won't cut it. I know you don't want to upset your mum, esp since you're living in her house. But I don't think that she will put you and her grand-daugther out on the street because you kicked your brother out. After all, you're family too. Rather than use his joblessness or bum lifestyle as an excuse for kicking him out, you could use health reasons. Such as: the apartment is too small for 3 people, not enough ventilation in the house, risk of carbon dioxide poisoning among the inhabitants, the doctor said your daughter faces the greatest risk and she could catch meningitis. You can't take that risk, that has always been the reason why you only offer TEMPORARY stay to visitors. Even if no one is convinced of your argument, you just hold fast and stick to your guns. It doesn't matter whether they believe it or not, so long as YOU believe it (so make sure you believe your own lie). Then proceed to give your brother a notice of a date to leave, say 1 week (where he chooses to go is none of your business). If he makes no plan to leave, after one week pack his stuff in a nice box and place them in temporary storage, then change the lock of your front door, or steal his keys if he has a pair. When he comes home and knocks on the door, send him a text telling him where he can find his belongings because his notice has expired. Problem solved. If your mum complains, throw the health reason at her, surely her grand-daughter's health is more important than her concern for where her adult son is staying. Reassure her that your brother knows plenty of people that he can squat with before he gets a job (even if it's a lie). Also, tell her that she is welcome to take him in if she's that concerned about him, but really, he's a big boy and can take care of himself. But let everyone know, in no uncertain terms, that as a parent you must protect your family (doctor's/health inspector's instruction).

Unless you have a standard lease and are paying rent you can't, this isn't your house. What you could do is move out and find a new place for you and your daughter.

you rnight not be able to if its your rnothers house, rnaybe you can rnove out yourself

Unless you're paying your mother rent, you don't have any legal standing to kick him out, and there's no way you can get rid of him without family drama, short of hoping for an accident or that he is arrested.