How to manage working a full-time and part-time job?

Oh man! This sounds like a pretty stressful situation for you. Perhaps you can ask to have your hours changed at one of your jobs so that you have more time to get to your second job. Either see if you can go to your morning job a bit earlier so that you can end earlier and have time to get to work... or ask your employers to allow you to start a little bit later at your second job (maybe ask to work an hour less each day at your second job so you have an hour to unwind and travel to your second job).

You stated in your answer that you need the money so it obviously isn't a viable option for you to cut your hours down by much. Unfortunately, that means you can't change your situation, really. If I were you I'd try to stick it out for a bit.. but look for a higher paying job in the meantime so you can eventually have a less busy schedule.

Another option is... you could look into working with the elderly, or special needs who need in home care. You don't need schooling to get this type of job. I live in a small town and we even have this type of job. They should have it anywhere. Anyways, some elderly/special needs people's family will pay you to come to their house and sleep there overnight, checking on them every so often. You get your own room to sleep in and you literally get paid to sleep. You just need to be there as babysitter for the person you are staying with. It's a fairly easy job that pays a good amount. Perhaps you could look into doing this for awhile until you get a better paying job?

I wish you the best! I'm sorry you have to deal with such a busy schedule. I know how much that can suck!

You can't. Neither employer particularly cares what challenges you have juggling hours. They are only concerned what you're doing for them. If you are unavailable at hours they need you, or burned out from the other job, that's not their concern. Be careful that you don't compromise your full time gig by adding a part time one.