Everybody is behaving normally for an abnormal situation. There are geriatric specialists who work with elders in this situation - usually a team of the doctor, the nursing staff, and the social worker. Depression in elders is common, as is frustration with the lack of mobility. Also, there is a sort of "situational dementia" that takes place when an elder is moved out of their home and into a hospital or rehab center. They often don't know where they are and get disoriented - then they realize where they are and they get angry. We went through this with my mother-in-law, and it was so helpful when the doctor explained it to us - we wound up being sympathetic (although frustrated, of course) but at least not so angry at her or bewildered by her. She kept demanding that we go to the supermarket because there was a sale on some ice cream bars. At first we argued that she had no freezer in the nursing home and couldn't keep them, but finally we just said we went to pick them up and they were all out, but that we would keep checking for her. That sort of thing calmed her down.
You might suggest that your father bring in some of your grandmother's things - nothing valuable, but some photos of the kids and grandkids would help. See if the other grandchildren will draw a picture or write a letter. Maybe a small CD player can be brought in, and the siblings can be assigned a week to be responsible to send a letter or a CD Grandma might enjoy. Your father, the other sisters, or even a staff member might be willing to put one in and let it play. If she has a DVD player, maybe they can watch an old movie together, something she enjoyed in her younger years. My mother-in-law loved travel movies - the story didn't matter, but "The Sound of Music" reminded her of Austria and "Roman Holiday" reminded her of her travels in Italy. If your grandma likes mysteries or historical period pieces, maybe the siblings can set those up - it provides a diversion and something to do besides listen to Grandma's rants about how miserable she is. There is only so much conversation they can engage in about the weather, current events, and all the other things Grandma is missing. She needs the break too.
Sometimes local agencies have "friendly visitor" programs where a volunteer comes in to read to the patient or just chat. Check with the senior center in that town, or the churches/synagogues. You'd be surprised what resources are available for those who ask. I'm in a local chorus that performs at nursing homes - we bring music in to those folks who can't get out. Sometimes a local elementary school or a scout troop or the high school community service club will bring in a field trip - the kids do crafts with the elders and do some seasonal decorating - construction paper flowers for the coming of spring, maybe bring in a flowering plant to spruce up the room.
The siblings who say "Grandma will get over it" don't realize that the average stay in a nursing home isn't very long - people go downhill pretty fast if they cannot rehab. A short stay for a broken leg for a strong person is one thing - persistent paralysis or something that doesn't heal usually results in a shortened life span due to medical and psychological complications, sorry to say. However, your father cannot continue to stay overnight and I don't think it's helping anyone. The nursing home or Elder Services should be able to give information on respite care - giving a break to the caregivers. You can help by making phone calls to those agencies, and by having your father (and grandmother) give you any necessary permission to talk to the resources available. The 2 sisters who help out in the evenings should be willing to sit in a meeting with the social worker (or other elder care specialists) with your father and make a plan. Then THEY can give this info to the difficult siblings so that the family meeting isn't just involving their opinions but also the specialists' recommendations.
Those siblings who still abdicate their responsibilities should be left out of the discussions and decision-making. If their opinions just upset everyone, try to understand that it may be their way of saying they cannot deal with the reality of Grandma's condition. They may fear her demise and just deal with it by being angry and oppositional. They will ultimately feel guilty and probably do now anyway - but they handle it by being argumentative. Don't try to convert them. It takes too much energy.
i know you feel helpless but you are trying to reach out to your father, and that's a good thing. Don't overwhelm him with all of these ideas at once, but maybe try to set up a conference call with his two helpful siblings and him, and see about assigning tasks. Organizing a "schedule" of letters or little gifts and "assigning" them on a voluntary basis to the entire family will give them something concrete to do - they can do it or ignore it, but don't ask for their opinions or criticism. Just say, "we're setting up this really fun chain of activities for Grandma, and we know many of you want to participate but not have all the letters/cards stack up on the same day. We want to spread it out so she gets something every few days over a period of time. If you want to join in, great."
Doing something very small and manageable, but positive, will help everyone through this situation.
Good luck!