C.H.
I also had a mom who refused hospice. One day she phoned me and my sister and told us it was time to go to hospice. (Her bedsores were too extreme for her to handle, and she didn't have home health care.) We took her to hospice. She became comatose (in and out) the next day, and died eleven days later. The kids handled it just fine. I remember it was quite a juggle getting everything done -- the kids were 2, 4 and 7. I mostly needed husband/friends/neighbors to watch kids while we visited her.
One thing that I would caution, and this is HUGE. If she has an advanced directive stating "no heroic measures" such so no water or nutrition, get her to agree to TEAR IT UP. Just like Terri Schiavo, my mother essentially starved to death before our eyes, and there was nothing we could do to stop it. It was outrageously gruesome to witness. She had cancer in the throat, and couldn't swallow, but she was alive and mildly responsive during the eleven days that she starved and died. The doctors kept telling us that she'd "die today", or "in a few hours", or "definitely by tomorrow". They were all wrong.
If they'd fed her intravenously -- even just water -- she would have been so much more comfortable, and would have died from the cancer instead of from starvation. But she'd signed that Advanced Directive, having no idea what it would do to her.
As for your Dad and siblings, since they're not willing to let you take charge re: decisions, just do your fair share and stop making suggestions. They've all heard your opinion and unfortunately they are not brave enough to face hospice either.
Be calm in front of the children and don't let them know that you're annoyed with the relatives -- that will only add to their tension.