Travis’ advice is dead on here. In a perfect world I would say that you should widen your tires, but this probably is not an option for you. Some tractors have rear axel extensions that widen the wheel base. If this is an option for you it might be worth considering. BTW, what tractor do you have and how is it set up? Do you have a loader? Do you have ag, turf or industrial tires? How much hp do you have? These pieces of information can be helpful.
Regarding the front axel, most every tractor I have ever seen has an axel that pivots about a center point. As an example of this in action, if the tractor is merrily going straight over flat land but hits a pothole on the right front tire, the front axel will pivot down on the right side so that all 4 tires maintain contact with the ground. Alternatively, if the right tire hit a bump the axel would pivot up on the right side. Without this feature, any time you hit a bump, dip, or any uneven patch of ground, the tractor would lose ground contact with at least one tire and possibly even two tires. The front axel almost acts like a sort of suspension for the front of the tractor.
I just want to reiterate what Travis said about properly weighting the tractor. Whenever I operate my tractor on even marginal side slopes (say 10 degrees or so), I always lower my loader as far as possible, sometimes just barely clearing the ground. On occasion I have been known to put some weight in the bucket (not on top of) to get some extra weight as close to the ground as possible. The weight should be as close to the ground as possible, but especially try to get the weight at or below the level of the axel. I asked earlier what type of tractor you have partially for this reason. If you have a subcompact tractor it will likely have a low center of gravity, but those small front tires can give a bumpy ride over uneven ground. Generally, the larger the tire, the smoother the ride over uneven ground.
Last question. Does your tractor have a ROPS (roll bar) and seat belt? In my opinion, a tractor without a ROPS is inherently dangerous on slopes, and a seatbelt can be a literal lifesaver.
Pearl, I have spoken a lot here. I love my tractor time and always look forward to more, but they must be handled with care and skill. Care you can manage immediately, skill only comes with practice. Your caution is well warranted, but I am certain with time you will master its use.
Good luck and safe mowing,