For OP, couple of positive thoughts to balance work, riding and your health ( physical and mental) for where you are in your life right now.
Pick 2 days a week to make the drive. That would get you 2 days a week, which is probably the minimum acceptable on the riding side and not run yourself ragged. Maybe every other week you pick up a third day? Maybe only once a month pick up that third day but that time will add up as you go.
If you have sone extra days off, schedule a sort of mini bootcamp, drive and lesson everyday for, like, 4-5 days. Always made huge progress doing that…not sustainable for more then that 4-5 stretch due to other demands on my time but well worth it.
Other thing is those close by Western barns. Disagree it will retard your future hunt seat progress. Yes there are differences but you are an Adult and can adapt. I rode Western for 15 years, was pretty good, especially in Trail, Western Riding ( pattern class with multiple lead changes) and a little bit of Reining.
Then had to take an almost 8 year break and ended up in the Northeast where there were no acceptable Western trainers within several hours but a good selection of quality H/J barns and educated trainers within 45 minutes. Yes, it felt awkward at first but Western taught me to feel where my horses feet were, feel the leads and manage strides. I got pretty good pretty quick. Even when traveling for a living and riding 3 days a week on average.
If you find an educated trainer, the Western option can mean more quality saddle time to allow you to develop as a thinking, competent rider.
Will say that for where you are right now. I would not recommend mixing the disciplines right now. True there are riders, including Pros who do both but they are already quite experienced. Pick one for now, you have many years ahead of you to experience and learn as much as you can about partnering with a horse and which discipline really works best for you and gives you the best access to quality programs,
Oh, Dressage barns might work too, if there are any nearby with legitimately educated trainers. Again though, you do not sit on and communicate with the horse the same way.
The trick is finding the right trainer with the right program centered in solid basics and sometimes you might need to compromise on discipline to find that unless you move,
Remember, bad, ignorant trainers running crap programs WILL retard your progress as a rider and can haunt your riding for life. For now, ride as often as you can whatever the best trainers near you teach. Good basics are good basics.