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He's 36, although he is in many ways emotionally immature. We get on fairly well but he's never taken criticism well. I wondered about parenting books. I think he would point blank refuse a parenting course and if he did go would probably spend the course arguing with the teacher. One concern is that he lacks insight - I honestly don't think he thinks there is a problem and is anything thinks the kids are "naughty" (which they aren't, even by normal toddler/pre-schooler standards). One issue is that my dc is only a baby so I can't really talk about how difficult I find these things to manage. I could lend him a book though and just say it was a really good read and lots of interesting tips that he might find useful (I wondered if The Incredible Years might be a good start but suggestions welcome). Another thing I could try is seeing if my dh would talk to him as he really respects my dh's opinion but I'm not sure dh would agree to it. I should also speak to one of our siblings about it and see if they have any suggestions.
How old is he? He sounds quite young. Your brother is also going through a tough time, it must be humiliating to be thrown out by your wife and have to move back in with your parents. You say he only sees the children a couple of times a week, and that he talks about them fondly. When he brings them up, say something like, "and you see them for so short a time you must make it precious, not waste cuddle time arguing"
Without knowing your brother or your relationship, it´s a hard one. I would suggest trying very gently to become or be (depending on your relationship with your brother until now) a trusted person for him. He is obviously going through difficult times. The ways he is handling things and treating his kids are obviously awful but if you try to tell him what to do, it sounds like he will just shout and block you. I think you don´t have much you can do, but if you can gradually work yourself into the role of a trusted shoulder to cry on, someone who will listen and not judge, you might be able to take some of the pressure off him and he may become more relaxed generally - and hopefully with the children. My big hope would be that you would win his trust enough that he might ask you for advice for dealing with the kids or that you could end up in the kind of situation where you could feel confident lending him a parenting book "because it´s really good" (not criticising him or anything...) or suggesting him and you doing a parenting course together, without him feeling attacked.
My brother and his wife recently separated and he has moved back in with our parents. They have not yet divorced or sorted out anything financially, so he still gives his wife all his salary. They have 3 small children (age 3 and under) who my brother sees twice per week, once at my parents' house. He isn't paying my parents any rent as it transpires that him and his wife are in debt, partly because they bought a large house they couldn't afford. He is very disorganised and driving my parents mad as they cook, clean, do his washing and get him up for work as they worry he'll lose his job and the financial situation will be even worse. When his has his children round he often shouts at them and rants about how they are "winding him up" and doing it on purpose. He does love them and talks about them with great fondness (and to them a lot of the time) but he can't seem to understand that a 3 year old isn't capable of behaving like an adult. He puts the older two in time out repeatedly and they don't even understand why. He shouts at them when they have toilet training accidents. This culminated in him locking them in the bathroom at my parents house for bad behaviour. My parents were appalled and told him to let them out and he shouted and swore at them about how he knew best, they had to learn, my parents had no idea (they have 5 grown-up children and countless grandchildren). Despite this his children do miss him terribly and try to block his way from leaving or hang onto his leg when they are being picked up. The older two have also just started nursery for the first time and are toilet training so it is obviously a stressful time for them (which we have pointed out to db without success). What can I do to improve this situation?