Suffering caused by uncertainty of whether actions will cause more or less physical pain to dying family member?

Personally, I don't think you are worrying about the right thing. Whether you are easing the pain enough or not. Is not the most useful thing to worry about, IMO - given the circumstances.

My father passed away a while ago, and it is too late for me to fix it now. But I think the most important thing to worry about is having some of your fathers best ideas disappear with him. If I were you I would spend this time listening. This way I would be able to ensure that these things lived on. Whatever I learned from my father is alive in me now.

I think part of the Buddhist doctrine is that you should try to do what's ethical -- decide what's ethical, the "right" thing to do, and do that.

And then even if the outcome is sad, at least you don't regret (or feel remorse about) your action -- because your intention was correct, you did the best you could or knew at the time.

What's considered "ethical" is spelled out in some detail for monks. I believe it includes looking after each other in times of sickness ...

Monks, you have no mother, you have no father, who might tend to you. If you don't tend to one another, who then will tend to you? Whoever would tend to me, should tend to the sick.

Buddhism is less detailed on the subject of lay ethics, but I believe it does include supporting one's parents as may be possible (SN 2.4 and DN 31).

It may be that the right thing to do -- or the best you can do in the circumstances -- varies from person to person, time to time, place to place.

I'm sorry to hear you feel responsible for managing physical pain, even though you're not a doctor.

• When I've been in a situation like yours I understand it's my responsibility to ask the patient, "Would you like me to take you to see a doctor?", and make another appointment or perhaps go to a hospital's Emergency department with them.
• I feel it's also my responsibility to understand the doctors' diagnosis, prognosis, prescription, and care plan -- especially to whatever extent the patient can't -- to help the communication between the patient and the doctors and nurses.
• I also want to not cause the patient unnecessary worry or grief, when I'm with them and able to talk with them.

I don't want to tell you what a doctor should, but my understanding is that one should expect pain to increase as cancer progresses, and doctors should expect to adjust the prescription as time goes by. I'd generally expect from my experience that a doctor will change the prescription only when they see the patient (i.e. not without seeing the patient), so when you think it's time for a new prescription then it's time to arrange another doctor's visit. I also expect that nurses (or sometimes other care-givers like family, if they're told how) might administer a prescription -- count pills, keep an eye on the time of day -- but only a doctor decides what the prescription is.

You might find this helpful too -- What nurses need to know about Buddhist perspectives of end-of-life care and dying.

I think I read somewhere that on average fewer opiates are used/prescribed in palliative care in Buddhist countries. I can't tell you whether that's good or bad, I suppose it's a topic for doctors and patients (and families) to negotiate in specific circumstances. There's a little mention about the trade-off in that article for nurses -- see the paragraph which begins "Taking into consideration overall well-being" ...

However, if severe uncontrolled pain develops, cognitive impairment (e.g. delirium) may result that may require the use of strong opiods for effective relief to achieve the best cognitive function possible that would support meditative spiritual practices. In concordance with good practice and recognizing that the individual needs of each patient will differ,nurses should continue to monitor the need for pain relief, and should clearly document the preferences of such patients with regard to pain relief, particularly during initial patient assessment regardless of the setting (patient’s own home, hospice, hospital).

... though I imagine that's an "FYI" for nurses and the actual decision is to be made and agreed between the doctor and the patient (or the family who acts as the patient's "guardian" or "parent" if the patient isn't conscious enough to decide).

Also I'd add that so far as I know, doctors are quite careful not to kill their patients -- not to give an overdose, too much too soon. Part of what happens is that the patient's tolerance for the medicine might increase -- which is sometimes part of the reason why the doctor can (safely) and/or must (for it to be effective) increase the dose -- but it's the doctor's job to know how, what, when, and how much to prescribe, so that it continues to be effective (beneficial) without being unduly harmful.

Lastly it may be worth mentioning or remembering the brahmaviharas. According to this author

These four attitudes are said to be excellent or sublime because they are the right or ideal way of conduct towards living beings (sattesu samma patipatti). They provide, in fact, the answer to all situations arising from social contact.

I think that the four include, "I don't want to harm you", "I admire your goodness" (as well as, "equanimity").