I am very sorry and saddened to learn of your sister's and family's recent loss of "Max." Welcome to this forum despite the unfortunate and heartbreaking circumstances.
Accidents such as what you have all experienced are much, much more common than people think. Especially on farms & ranches. I come across posts from those who have lost their pet's to accidents like your family (and brother) witnessed, quite often. They are heartbreaking "Freak accidents" and they DO happen. Stories are shared here and on other Grief Forums. I read of one recently where a farmer whose beloved and loyal dog had rode with him on his tractor each day for over 12 years, which tragically fell off of the tractor they were riding on and was drug under and killed by accident. Needless to say it was a devastating loss to the farmer.
I think many here would agree that "Freak accidents" are probably one of the most difficult types of grief that one can cope with and try to overcome. We all struggle here with the "What If's?" Those whose beloved pets pass away naturally, or those whose pet's have to be put to sleep, usually due to a terminal diagnosis or a myriad of health issues, but "Freak Accidents" involve an even deeper level of "What If's?" as they seem so, so avoidable, when one who is experiencing grief begins second guessing what occurred and their actions or inactions at the time of the accident. "Second guessing" is part of the grieving process for all of us. Each of us must process it / work through it, and come to terms with ourselves.
The truth is, with "the law of averages"?, the fragility and vulnerability of our little ones? and their often completely, unpredictable behavior at any random moment? Such as running where they are not supposed to, being to inquisitive / curious, getting in the way etc. - accidents ARE going to happen. It's just the very, very sad truth. As we all know, it only takes a matter of minutes, or even seconds, for an accident to occur. So your brother, your sister and your family are NOT alone in this experience or his grief. As I wrote, I've read it time and time again posted and shared here on Grief Forums like this one, and on others.
I personally experienced near death accidents with my cat "Marmalade." Who used up 9 of his supposed "9 Lives" directly in front of me. He finally ran out of "Lives" in the end. Ultimately his declining health was the result of him choosing one night, to enter into a vicious Tom-Cat fight with the neighborhood bully cat named "Blackie", who had just assaulted "Marmalade's" girlfriend cat "Star." He sustained an injury that never healed right and he required invasion surgery, which resulted in him having an evident stroke on the operating table. "Marmalade" never fully recovered after that and went downhill. But my cat chose to do, what HE wanted to do at that moment. He opted to run past my legs and out the rear gate of the warehouse we were living in (for the first and only time) to get into that vicious Tom-Cat fight in the middle of the street. To him, he would have considered that a "Good Death."
I'm sure at the moment that your sister's dog "Max" was unfortunately killed by the tractor, he was totally enjoying himself. Running free on a farm!!! What a remarkable experience that must be for any dog. Even for 1 minute or 1 hour or 1 day. And Max was 11 years old. How many GOOD days did he have? Most likely thousands of good days & nights. And he was part of a loving and caring pack. All dogs should be so fortunate. : )
I hope your brother and sister and the rest of your family continues to travel through time and heal, and that soon only good memories of his beloved pup shall remain. You Mother is what they used to call" "Of Pioneer Stock." She is a very brave and compassionate woman to have put Max out of his pain & suffering the way that she did. So strength and courage runs in your family. You will all need to tap into that strength and courage now. It is in your DNA, which is comforting.
It may help for your brother to visit this grief forum and some of the others and read of others experiences and grief. It has helped hundreds if not thousands of people who have experienced grief. You or he can also search under "Accident" to read of what others have endured and ultimately healed from, and survived. Including this one:
It would be good if your brother knew that he was not alone in his grief. This seems to be helpful. I am sorry for what Max went through and for your brother, sister and your family's loss.
Kind regards & my sincerest condolences,