You need much more air in the tires since it is bottoming out and causing the snake bite tube failures, which can also cause damage to the tire and rim. There is good gravel and there is bad gravel, hence 'your' riding conditions and expectations dictate the ideal tire width, of which personal preference also makes a claim. But let's start with the snake bike problem which is happening frequently from the sounds of it and that points to running too low of a pressure.
Appropriate tire pressure, for the team weight, is of course determined by.... the 'team weight' and the 'bike weight', combined. Whether your tire and rim combination is up to handling the actual needed pressure to support the team (and the loaded ready to ride bike) is another thing. Tires on a quint (5 person bike) with adult sized riders, supporting the vast majority of a 1/2 ton of weight on 1.5" (38mm) tires, needs a minimum of 120 psi, to be steerable and rideable, with regard to the front wheel. Ideally more would be better, both front and rear, but the 120 psi pretty much maxes or exceeds, at least on paper, the capability of available components, i.e., rims and tires. That is of course an extreme yet real life example. A typical somewhat light to middle weight team of say 180 captain and 110 stoker would balance out well with near equal weight front and rear on the wheels with 110-120psi in 28mm tires working out as a near ideal pressure. A 32mm on the rear, with the same team, works well at 95-105psi. Just my 200,000+ miles and 38 years experience being shared. YMMV
Try this -->> To determine your needed tire pressure, put a scale under the front wheel and read the weight with both of you mounted up. A helper and a wall come in hand here! Repeat for the rear. Then apply that new found info to this chart and see what tire pressure would likely work out best for your total weight / tire width combination.
https://www.precisiontandems.com/pho...tirechartx.jpg
There are many online pressure calculators available these days. I am confident all of them will say that more air pressure is needed.