G. Mark’s Answer
First, I'll give you the general answer about working two jobs at once. Absolutely. As someone who worked three jobs while going to college full-time, I know it can be done. Granted, two of those jobs were part-time, and the kick was that those two part-time jobs were directly related to the major I'd chosen. Now, the limiting factor there was the actual number of hours in a week. This requires that you plan your schedule carefully. There's a great probability of those jobs clashing in time and in terms of pure human energy. Having jobs in stuff you already like is a huge advantage. One of my jobs was loading trucks for a shipping company, so by the time I got home, falling asleep was not a problem.
Now, since you're talking specifically about animals and therapy and psychology, my opinion is, contrary to some, that there is a lot of overlap. I also know that getting involved in those fields a part-time basis is common. A way to increase your probability of success is to seek co-op and internship positions with companies involved in those activities. Starting out that way will give you much more leverage in being able to tailor your hours. And these activities don't necessarily have the hourly limitation that, say, working in a commercial/public business would. Some of those activities could be required around the clock at times. Being "on-call" would allow you some flexibility, BUT also consider that you would have to peg out hours when you would NOT be available, and that would have to be worked out with your employer(s).
Finally, let me tell you that what you're proposing is a significant challenge. And due to the many things that could go right or wrong, you need to be prepared to be unsuccessful in gaining a part-time position in either of them. On the other hand, that failure is not permanent. You might be successful in getting that second position at any time in the future.
Bottom line: Yes. Not easy, but yes.