Not much different with your set up than with ours when our kids were little. The only difference is, we were in a pop-up. Daughter slept on the smaller pull out bed, son slept on the table turned into a bed. Neither had individual "space", and actually we, the parents, did not either. We had a mini-van that towed the pop-up and we kept our clothing and personal items in totes in the back of the mini-van. We also carried a pup tent with us and that became extra storage space for lawn chairs and such once the pop-up with raised.
The real bottom line is, there is NO privacy in a camper. Not knowing how old your kids are, the younger they are the more likely there will be less conflict and demand for their own space. If it's acceptable, have both kids sleep in one bunk and use the other bunk for storage. According to your photo, you have space under the bottom bunk for storage containers.
And one more thing, not only for you and your spouse, but your kids also have to accept the fact, in any RV, you simply cannot bring "everything". There is no space. This is one reason why everyone in the family unit must be in agreement and on-board with the RV "thing" from the very beginning, not after the purchase and then they are forced to comply... "Resistance is futile???"
If your kids are older, they simply have to understand this. If they are younger, they have to be taught to share the space.