I've done this but it is a bit like peeing into the wind, especially if you are camping with friends or family.
Given that you want to get away but it is not doable to let go, I have two suggestions:
1. Make a plan to partner with someone so you can cover for each other. Life happens. You cannot be on call 7x24x365 forever. You won't like it and eventually your customers won't either. Certainly the significant people in your life will hate it. Get involved with a consulting partnership or form one yourself. If you like this way of working then make it work long term.
2. On call camping is all about planning and setting expectations. What is your on-call response time? 15 min means you can find a campground with some kind of connectivity coverage and stay there. Enjoy sleeping and eating and hanging out in a semi-isolated location. If you just have to check in every 24 hrs then you have a lot of flexibility and you probably won't have to bring much special with you.
Low end: Just bring your cell and data plan, or scout out local wifi. Most park/camping/resort areas will have a small town nearby with various wifi options. Coin laundries have excellent wifi connectivity in my experience though usually not free.
High end: eh, under $1000 investment. Wilson cell boosters. Omni and directional cell antennas. 3g tends speed tends to be distance dependent and will slow down even with good signal. LTE is much better. I have made connections as far away as 80 miles. Horizon gets in the way usually but it helps if the tower is on a mountain top or if you are. Portability is a challenge but you can set up a backpack unit fairly easily with, say, 5Kg of extra booster, battery, charger weight. Or go wifi: ALFA wireless units with 1 or 2 watts and a good directional antenna can get you wifi at amazing distances but are limited because most access points are not set up with antennas outside a building. 8-> They tend to be low power and indoors. Portability is again an issue but doable. Climb to the top of Pyramid in Jasper and camp there. Line of sight will not be an issue but nail your tent down.
Higher high end: $2000 to $10,000. Satellite internet with a portable gps enabled self tracking dish in a fiberglass dome. You will probably want a portable generator. Also need a data plan at about 50 to 100 per month. You could carry a dish and transponder on a hike which would be awkward but could be quite fun. Tends to tie you down and prevent straying far from where you set up your base camp. Speeds can be quite good for streaming but ping times are in the 1000s of milliseconds. Usually have to pay a premium if you go over a couple of GB per month. Oh and usually a 1, 2, or 3 year contract. Um, and mountains can be an issue if they block the satellite view. Choose a North/South valley.
Ridiculously expensive high end: $100K or more. Bring your own tower and cellular repeater site. Get a trailer with a 40m telescoping tower, hydraulic stabilizer legs, and a mini network center. You should be able to get LTE almost anywhere with the correct setup. Add in the satellite transponder as backup. Camp near a fast moving mountain stream and setup a hydro electric supply. Plan where you are going to hike and run your own repeater with directed coverage to the area you will be traversing. Put a booster in your pack and attach a 2 meter buggy whip so you have continuous coverage. A blinking light on the top will aid rescuers when you get lost. Check regularly with your doctor for radiation induced growths in various locations on your body. Be aware that national park wardens take a dim view of this sort of setup.
I handled on call with a Wilson cellular booster in my truck and a portable wifi router with a 4g dongle. As long as you can get one bar on a cell results should be very good. I stuck around the campsite, drank coffee, cooked food, and read books. Nice but not full on hiking/camping.
Again, the best choice is leave it all behind. The most complex issue to deal with when camping should be how to make a banana boat on a campfire.