From what you are describing and lightly probing the energy my interpretation is that you have multiple layers of convoluted negative beliefs, most likely in the form of generic, seemingly shapeless doubt. Your family member most likely holds a similar pattern, perhaps picked up from the same source a generation or two above you. Perhaps an aunt.

It is perfectly natural that when you focus energy in a direction that represents a particularly large shift towards a new reality that anything that contradicts the shift would come to the surface, in the form of a consciously intense negative feeling.

It is also perfectly natural that someone who you are emotionally close to would pick up on your feelings- especially when that persons holds similar belief structures.

Further, it is perfectly natural that a person's body may respond with illness to focused negative emotion.

So far so natural. There is really nothing surprising or crazy about this situation- on the contrary, it is fairly typical, right up to experts chosing to ignore the energy connection.

I would recommend to do two things: One, eliminate the doubtful beliefs within yourself, and two, consciously connect with your family member and send positive suggestions. The first is the actual long term solution to your problem, because if you no longer hold your negative beliefs, you will no longer have the negative emotion, and your family member will have nothing negative to react to. The second is a metaphysical first aid measure that will neutralize any negative suggestions you may be broadcasting while you are working on your beliefs.

Clearing Negative Beliefs

To clear your negative beliefs, I use three techniques frequently: Bashar's method, symbol healing, and blanket forgiveness.

Bashar's method says that you act on your highest excitement, to the best of your ability, without being attached to a particular outcome; you seem to be doing that in your requests. Then, when contradicting beliefs come up, you allow yourself to feel the particular pattern of negativity in a lot of detail, and when you feel you comprehend it, you ask yourself: What would I have to believe in order to feel this? You may have to probe several times and insist on a simple, clear statement, but once you've got it, you will most likely feel the energy dissipate, because negative beliefs don't survive very well once they have been clearly and consciously exposed in all their absurdity. Repeat this whenever you feel strong negative emotion.

The second is symbol healing- you start the same way by becoming aware of the details of your negative feeling, like a certain tingling in a certain space in your body, or a dullness in one place combined with a sharpness in another place. Absorb the pattern, make yourself aware of it, in more and more and more detail. Then, instead of asking for a sentence that describes the belief, ask for a symbol. You will most likely receive some kind of nasty symbol- it could be quite specific, like a hammer hitting something, or it could be more abstract, like just a bunch of lines. It doesn't matter. Once the symbol is reasonably stable in your minds eye, absorb it- study it a little bit. When you feel inspired to do so, start making changes- shifting things around, rearrange the lines, change the hammer into a feather and the anvil into a pillow, change a roving dragon into a purring cat, a violent storm into pleasant lush landscape, anything that makes you feel changes- it's all just an excuse to change the energy that you are feeling. Keep going with this until you feel a distinct and strong sense of relief, and a sense of completion. Then mark your process as done (some variant of saying "Amen" works well, like saying "it is done"), and go and do something fun, like playful imaginary energy work, or calling a friend, or solving a hard math problem (all depending on what you consider fun).

The third works best when you have a sensation that you feel aggression towards someone, or something, or a situation- some kind of destructive outward motion in your feelings, and a sense that someone or something else is morally inferior, or explosive or bursting negative feelings. You absorb your feelings in the same way as in the first two, and then, when you have felt them for a while, gently speak to yourself: Whatever this is about, it is forgiven. Whatever it is about- it is forgiven! Keep going until you feel a strong sense of peace where the aggression was. Mark the process as complete- Saying "Pow" and covering one outstretched fist with your other hand, from Hawaiian esoteric tradition, also works very well- and go do something fun.

Sending positive suggestions

Healing yourself by clearing your beliefs will also heal those close to you, because they will be receiving positive suggestions from you instead of negative ones. But you can also wag the dog- you can heal others by directly sending them positive suggestions, and that will have an indirect but strong effect on your beliefs. You can do any of the two, but when you just received note about a situation of a friend, like you described, immediately go directly to work on them for both their and your comfort.

A great way to do this is to decide for yourself that a color means peace, love, friendship, good energy, and happiness- green is the symbol for that in Hawaiian esoteric tradition. So you think about your family member, and imagine a large green glowing cloud of love forming wherever that person is, and enveloping your beloved person, and interpenetrating him or her, and filling that person with all that is good, and all that heals, and all that makes him or her happy, and that influences all that is going wrong to go well. All these things are the very nature of love, and from generations of practicioners, the color green reportedly works well for that. You can also use spotlights, and bristling intense lights, and lasers, and search lights, and beams coming from all the stars connecting above that person and focusing all their loving and healing energy.

Pink is also a great color to use, and it represents friendship, and the falling away and transforming of negativity and the blossoming of friendship and harmony. Both represent feeling, but the effects are distinct- you can try them on yourself to get a feel for which is more appropriate. A thick, pink fog is the preferred traditional pink tool- you pinkfog people and situations to make them better.

You can also use blue for calm confidence, red for roving passion, orange for sharp focus, yellow for lush sensory presence and violet for contemplative harmony.

In the end, which color represents whatever you decide it does, but the ones I suggested have been used effectively by a lot of people and I have chosen to use them that way too.

All these colors are symbols, just like in symbol healing, but they do stimulate a very real energetic effect. Try pinkfogging your family member in the hospital and place a green thoughtform love sun around them and make it brighter and brighter and brighter, and remind yourself that the brighter it gets, the more energy gets transformed. Then be open to noticing unusual positive effects that reflect the energy pattern change you are continuously performing.

When you have noticed improvement, and you feel confident that things are going well, go back to focusing on and refining new ideas and requests that excite you. And when you've done some of that, come back to clearing and greenlighting and pinkfogging. You are rather likely to have quite a positive spiral together by doing both as often as you can.