Your safety and the safety of others should be your main priority. There is nothing "set in stone" that says what you should or should not do when you have MS. I think it is a personal effort. Your neurologist might be a better "sounding board" because they will have a better idea of a "no-no" list.
For me, a horse is simply to high in the air and would leave me dizzy. Even a couple of steps on a step ladder can leave me off-balance. As for babies, if you are prone to dropping things, holding a baby while seated on the couch might be fine, but carrying a baby under the same circumstances could be risky and even riskier if you have a history of falling. You might have to decline to hold a child while going through a cycle of symptoms.
As to knowing when something is about to "hit" is, I think, a matter of knowing your body. As we live with our MS, we can begin to discover triggers and harbingers of attacks. For each MSer the triggers and harbingers can vary and it might take some due diligence to discover yours. A journal might allow you to gain some insight.
A hot pot? This is one area where I tread really carefully. I do not sense the heat and I have a scar on my right foot where a piece of slag burned through my sock and into my skin. I was unaware until I smelled the flesh burn. Nowadays, I am extra careful around heat and flames and doing anything in the garage.
You might give yourself some practice with some dumbbells to approximate the babies weight. This could allow you to strengthen your arms and to determine if the child's weight will cause a safety risk.
As to the horse riding, if you can ride, great! I would advise to never ride alone and to make sure that the other person is aware of your MS. There are many horse riding therapy programs with well-qualified staff and well mannered horses.
Great questions. I do not know if my answers can satisfy you completely, but I hope you can find a balance for your life!