Dear Anthony,
It is very hard to say how long your mom has, how rapidly she will decline. (Some people are tough - they hang on for a long time even after their body systems start to shut down.) But if the dr is recommending you bring in Hospice now, you probably are safe in assuming that at the very least he is expecting you will be needing a lot more assistance with her care, and quite soon.
It was my experience in nursing that when people reached this point in their illness, they could be very self-centered. Sometimes it seemed their struggle had them so internally focused that they really had difficulty seeing how the situation must be for their caregivers, and many still had a large dose of denial clouding their judgement, too. (Not intending to be unkind in saying these things - just realistic.)
For the sake of your mom's well-being, and your physical and emotional health, you may need to try to help her see that Hospice is not just about dying, but also about living - with dignity and as trouble free as possible until the disease process can no longer be held at bay. And that the decision to ask for more help is not just about how she feels, but also about what YOU need. The home health people can support you in this discussion, but it's best if the person who tells her that YOU need more help is you.
So, when you talk to her, tell her the same things you told us. Tell her that you love her, and appreciate her, and that you always will. Tell her you want her in your life for as long as possible, but that you also know she is not well, and you want her to be as comfortable as possible. Reassure her that YOU will be ok, should the day come that she is no longer here to watch out for you. (Moms need to know that they've done a good job in preparing their children for the hard stuff in life.)
Most of all, you have to tell her that YOU can only do so much, and you need more help to provide her with the best care you can possibly give her. Be firm - don't feel bad about telling her what YOU need. A broken caregiver is no good to anyone, but she honestly may not be able to see that YOU need more help, unless someone tells her it is so,
Sometimes it takes a gentle boost to allow a failing parent to still have a say in their life and also demonstrate caring for their family. Tell her that is what Hospice is all about: helping people to live well, while they still can.
I wish you and your mom and family the best. And remember, take care of yourself as well as taking care of her.
sincerely, tre