Can I combat this privately? Without fuss? Do I just need to get a grip?
Yes, yes, & no.
Your are not your dad.
Your exposure to his drinking problem is a factor in your own - but that is all it is - a factor. It does not define you!
As to "combat", & "getting a grip" - whew.
In a quiet, not-hungover moment, please sit with that phraseology a while, & consider how harmful it is to your own precious wellbeing.
You, for crying out loud, are a woman who has trained for marathons, raised children, held down a job, & taken a first step by posting about your relationship with alcohol here.
I'd hazard you already have plenty of grip.
"Combat" sets alcohol up as your enemy, with you as alcohol's victim, enemy, combatant ... whatever - this can only be a win:lose situation for you OR alcohol. (Clue - alcohol's a dirty fighter, & doesn't care about you).
Now view the alcohol not as some booze, but as the representation of the things you are using it to mask in your own life & psyche.
No need to beat yourself up for immediate answers. This is a long process, & all the better for it. When you asked about addressing this privately, without fuss, I'm guessing you are looking to avoid feelings of shame, or judgement by others?
The good news is you can do that, if by "privately" you meant you have funds to allocate to therapy. The even better news is, if you choose to do this all via local NHS provision - none of the professionals attached to your case will shame or judge you either. They will applaud you for taking charge of your own health.
Look at this as an investment in your own future & mental health.
Your aim should be less about "how do I control the amount I drink" & MUCH more about "what are the buried reasons I drink, that I have put a lot of effort into concealing from myself, because they are so painful?"
Does this make sense?
You are looking for understanding of yourself, & how to avoid the things that make you overindulge - rather than some magic bullet that will instantly stop that indulgence.
Behavioural science fact:
Observe a series of people walking a tightrope.
Call out to 50% of them "don't slip! don't fall off!"
Call out to the other 50% "great balance, keep that focus, well done!"
No prizes for guessing which 50% does better at staying on the rope ...
You can carry that metaphor into another mindfulness state. There are 2 ways of viewing yourself & your problems/hang-ups/addictions.
The first is a CONCERN MINDSET.
From here, you notice yourself, pay attention to how you are feeling, & develop thoughts like "I'm worried about my liver. I'm pissed off because I lost another weekend's training as I was below-par. I could have gone on that nice weekend away if I hadn't blown the budget in the pub."
The second is the SHAME MINDSET.
This would 'translate' the same feelings as above into terminology like - "I'm damaging my body but I can't stop because the booze has a hold of me & I can't get a grip. I'm not good enough to run a marathon because I'm too weak from booze & I have no willpower. I'm pissing money away & I don't deserve a nice weekend away anyway."
A CONCERN mindset will bring you to the aware, self-caring state where you can begin to make changes.
A SHAME mindset will keep you trapped in the cycle of resolution, wagon-falling, 'failure', shame, & back into the cycle ... ad infinitum.
Your GP would welcome you to an appointment to discuss how you are going to take charge of your drinking. (The medical profession likes working with self-referrers who are genuine about taking charge of their own health!). So no shame there - just concern.
You can ask for referrals to private or NHS resources.
If you can afford private (face it - how much more will it cost that the booze? What would you rather spend that cash on?), please do so, & bear in mind that it's OK to try a few therapists before you find the optimum therapy style & personality to work with.
You don't need more willpower, you need more understanding, & a trusted guide to hold your hand while you spend up to a year in thoughtful, self-rewarding care of yourself. There is a lot of expert help out there, & I hereby give you permission to seek it, & along with it - all the benefits of truly understanding yourself, your motivators, your fears & your triggers.
You should already be proud of yourself.
Go out & get some expert tuition in how to get even prouder.