For your brother, re-establishing contact might be best done via writting. That way you can really consider what you want to tell him and he has a chance to process in private. Your message should probably contain an apology, affirm that you believe him, explain your thought process in how you behaved and how you’re going to work on yourself to avoid falling into that thought process again. Then it’s up to your brother how he responds.

For your mum, the best thing would ve if you could get her to back off. I understand it’s difficult to be firm with your grieving mum, but anything you can do to be a buffer between her and Jeff could be helpful. Telling her something non-confrontational like ”Jeff is having a real hard time with dads passing, and in no position to help right now” might be best and isn’t techniqually a lie. If she pushed you can keep insisting ”no mum, Jeff is to upset to do and we have to make sure he’s ok too by not making him more upset”. Framing it as being considerate of Jeff will make it harder for her to keep pushing and will give you and easy out of being more involved. Also, avoid JADEing (justify, argue, defend, explade) as it will only drag it out.

Lastly, it’s okay that your image of your dad and Jeffs image is different. You can believe and respect Jeffs experience whilst remembering and appriciating your own. Just don’t do it in front of your brother. The emotions and confusions you feel about your dad as a person is probably best dealt with away from your family, who will not be able to stop themselves from trying to push their own image or judgement on you. Whatever you end up feeling on your own is ok, as we are complex beings and can recognise someone was a bad person and still love them for who they were to us.