Bereavement affects everyone differently.
I suspect your friend's focus on her brother's behaviour is deflection:
There are times in the natural grieving process for the individual to feel frustrated, trapped, and hurt. It is common to have those churning emotions surface and be directed toward someone or something. When pain dominates the feelings, it is natural to look for someone to blame. Being angry is a way of releasing energy, of protesting a loss that does not make sense or seem fair. Even though deep down one understands that anger is not logical or justified, emotions are rarely logical.
Once the individual has stopped denying that the loss has occurred, the reality of the situation begins to set in, bringing additional confusion, frustration and pain. The mind and body begin to deflect the pain, expressing it instead as anger. The anger may be aimed at an inanimate object – like punching a wall or kicking a trash can. It may be aimed at people; complete strangers, friends or family members. On occasion, the anger may in fact be aimed at the deceased loved one, emotionally distraught because they left us. Anger often is a cyclical process. One feels guilty for feeling angry, which of course only leads to feeling more anger.
Are there things that can be done to assist in coping with this anger?
Here are a few suggestions.
First, try to understand if there is resentment or disappointment that is fueling the anger. Perhaps there were expectations that friends would be more sympathetic. Resentment can occur when one person seems to have gotten over their grief more quickly. How many of the angry feelings are directed to people who did not live up to expectations during the time of loss? Were there things that were expected to happen that did not? Were the expectations reasonable? What are possible reasons that people reacted as they did?
Second, discover ways to release the angry feelings in appropriate ways that will bring no harm to any individual. Some people find that release through physical activity. Sports, physical labor, or intense exercise may help in processing and releasing the anger. Others may find that a creative outlet – music, art, or writing – may be the perfect way to express things that are often inexpressible. Don’t hesitate to reach out to others for support.
www.econdolence.com/learn/articles/second-stage-of-grief-anger/
The brain works differently when grief enters your life. The need to control can rear up and destroy relationships. People get wrapped up in their own emotions and communication comes a cropper. Families can spiral into animosity with all of these factors at play.
The sister needs to ask herself if she is being reasonable or if what she is feeling and perceiving are part of a predictable pattern of grief and self protective anger. It's sometimes easier to sit with anger than to sit with the pain of loss and the anxiety about an older parent, plus anxiety related to the future.
What is the brother to do apart from cutting the grass and maybe handyman jobs that he may or may not be any good at (most people farm out a lot of repairing/painting/fixing TVs, etc)? Is he to also bring over food - what your friend is most likely asking there is that his wife prepares food for her MIL.
Same goes for items like the broken TV - can he nip over on an evening to fix a TV or sort the issue when he has children, their schedules, piles of homework and prep for his classes to do nightly?
Is he to foist evening childcare on his wife (who probably has homework to mark and lessons to prep for her next day on top of the DCs' activities or bedtime) so he can go to fix a TV, all unplanned?
I also suspect that he cuts the grass on his weekend, and it then grows in the intervening time, so your friend sees grass not freshly cut. It would be knee high or higher if he never did it.
Wrt 'I don't like to ask Brother' - grieving parents are not always fair in their expectations of what children will do, and not always honest in their account of what individual children do. When talking to each child, an older parent may give one an impression that they are fine, need no help, all is well, when actually there is a list of stuff that the parent is going to ask the other child to do. Then they may badmouth one child to another, or point out things the other child has not done. A cycle of blame and recrimination and guilt and anger is fueled.
Grief affects everyone differently.
Ultimately, it might be best to help the mum get back on top of her own life - back to shopping, cooking, managing her own time, maybe connecting with resources for senior citizens and branching out into a new social life.