How do you manage working a full-time job and being a caregiver?

It's called caregiver burnout. Talk to Mom's caseworker about what other options are available. Ask friends and cousins to give you a weekend off. At some point she will need a skilled nursing facility. You have to preserve your own wellness first, or you can't take care of anyone. Hugs to a good daughter.

Please remember that caregiver work never takes a holiday break. It is 24/7 365 days per year. I don't think even a Saint could survive the work.

I did this for five years and I know how frustrating it can be. I had trouble with caregivers coming late or just being lazy and/or stupid. I finally just quit my job and went for seven months without an income, until retirement age was met for my teacher's pension. My SS wasn't available for several years. Adult daycare might be a good option for you. Then you could use the caregiver in the evenings or on weekends. I couldn't use it because my husband tried to wander away too many times for them to take him any more. Even though I'm at home now, I still have a caregiver come in 6 days a week for 3 hours. I can get groceries, see the grandkids, take care of personal stuff, etc.

Oh yes it's possible. But the toll is great.
My husband and I own a large garden center/landscaping company which we started and then successfully operated together. Four years ago, my wonderful husband died. My son and I now run the business.
Think - extremely seasonal business.
In spring, we are ridiculously busy, busy, busy.
My husband and I built our house right at the garden center so I am "always at work" and as the owner, I can assure you that my work is never done.
My business office, phone, time clock etc is in the basement and I work there all day. This time of year the phone is non stop. Payables/receivables also non stop.
My MIL is bedbound upstairs and I run up and down the steps a hundred times a day to take care of her, check on her, etc. At days end, I am exhausted.
I am lucky that she is now at the sleeping/staring stage and has very few words but the caregiving still wears me out.

So...............I understand how it is to work full time and be caretaker.

Also, my own mom (88) lives alone and has no car so I briefly run over to her house delivering groceries etc.

i didn't very good at it. If i had one sibling to share it with, it might have made a major difference, but i was it. I held down my job but my husband didn't care for my father so he resented the time i spent with my father at memory care. My dad died on New Years eve and my husband left the next day. I got served divorce papers 6 weeks later. I am in therapy and know i did the right thing. It was tough, and it still is, but at least i am slowly getting my peace of mind back. Hardest part of my life was when i lost my mom when she was 26. Second hardest was when i lost my dad at 92. Sometimes you put one foot in front of the other, shift your weight, and do it again.

If finances are tight, I'd definitely look into Adult Daycare or Senior Center, where she can hang out for a few hours a day. This way, you can save your aide hours.
We are fortunate, b/c I work full time too, but mom is in Assisted Living. Even there, she will just stay in her room all day long and do nothing, so now I'm looking into hiring someone (paid or volunteer) to come visit her 2-3 times a week and just talk to her, go on a short walk w/ her, encourage her to join the activities.
You can also check your local churches. Sometimes they have volunteers or sociial ministry programs that are affordable.
Lastly, I'm taking care of myself now to prevent burnout and found a caregivers support group for adult children taking care of their parents with Alzheimer's or dementia. This may not change the number of hours you put into taking care of mom, but it will hopefull help you deal better and prevent burnout. I start my group in 3 weeks, so I am very hopeful.

Exhausted though you are, you are likely better off than the people who stop working. You still have a life, a job and a financial future.
Take as much respite as you can. Get help where you can, example pre-made meals, clean around mom as needed, less often in other rooms. Opt for a little free time over aspiring for a good housekeeping award for yourself. Best of luck to you.

If anyone is thinking about resigning from work in the near future, please read this...

Here are some things to think about if one is trying to decide whether to quit work to care for an aging parent.... on average if a working person quits work he/she will lose, over the years, between $285,000 and $325,000 which includes not only loss of salary, it also includes the net worth loss of the health insurance; loss of money being put into social security/ Medicare; loss of other benefits such as matching 401(k); profit sharing; etc. [source: in part Reuters 5/30/12]

I totally understand what you're going through. I work full time and take care of my mom who has dementia. At one point I was giving a aide 3/4 of my salary to take care of my mom in the daytime so I could work. A friend told me about a daycare where she could stay while I am at work. They have grants that can pay for some of the days and it is only $45 a day for the extra days. This place h as s truly been a blessing and mom loves being with others. They play bingo and do her nails. They keep them busy all day and she is tired enough to sleep at night.
The daycare told me about the grants on my First phone call to them. Call some adult day cares and see what they have to offer you.

I would suggest putting her in an adult day care during the day and using the Medicaid hours afterwards. This way she is taken care of during the day and you don't have to "rush" home after work. You can run an errand, have a little "me" time, etc.