Would you accept a job offer that would require moving quite far from mom if moving is not an option for her?

Yes. Your Mum is in a nursing home, they provide her care. If you are POA, there is much that you can do online.

My Mum is 85 and I would not hesitate to move if I get a good job offer after I finish my degree. As in I am looking all across Canada and live on the West Coast. I have years of work and life ahead of me, I cannot afford to give up opportunities for my own future.

Your mom is 84 according to your profile. She’s lived her life. You have every right to live your life now. You need to put your own well-being first. Don’t put your life on hold or make financial sacrifices. Do what’s best for you. If the job includes PTO, don’t be afraid to try to negotiate more than what they offer, and then you can use some of that time to visit your mom.

Hi Emaries,
I am writing from the patients perspective and will share a conversation I've had with my 4 children which range in age from 38-12 as well as my DW. Three of them are adults, though two are college age, I have also shared this with my 12 yr old daughter.
I was diagnosed 3 1/2 yrs ago with Early Onset ALZ at the age of 57. I've told all of them they need to make the moves that are best for their careers, and best for any families they have in the future. The last thing I want is for them to feel trapped in to having to care for me. My DW and I began planning for the future at the time we were engaged. Being in the income range of higher middle income we've saved and invested for the last 25yrs. No, it can never be enough.
The three adult men have been encouraged to put together plans for their retirement years and encouraged to buy LTC insurance while they are eligible to purchase it. Our youngest is a Special Needs Child, who is medically disqualified from purchasing LTC insurance.
We started educating them on the subject of finances since their early teens, and just beginning with our youngest. Her special needs do not involve any intellectual deficits, so she's grasping much of what we are teaching her. My advice to you, look out for yourself and don't put yourself in a position of jeopardizing you future life. No, that doesn't mean abandoning your parent. However, you have to be sure you are securing your own future. That is only being fair to yourself. My opinion. Best of luck.

Such a personal decision and this very much depends on the circumstances. I would not accept a job that would require me to move far from my mother. For one, I am her main and only caregiver - but when the time comes to put her in an elder care home, I would do everything in my power to stay as close as possible and see her as much as possible. We have always been very close, a team really. I understand she is changing and will change as the Dementia progresses, but I know I am the only person she truly trusts and relies on. I pray everyday that when she starts forgetting people, even when she doesn't know who I am, that somewhere inside of her she'll still feel the trust and love.
I would also very much want to make sure she is being treated well and would always be worried about her care so I would want to check on her because there would be hell to pay if I find anyone mistreated her.
I have always taken care of her so I will take care of her until she is no longer. That said, again, everyone and every situation is so different so I understand both sides. Just in my situation, I know I must be around for her.

I would, she has care and is where she needs to be, you need to go on with your life.

Your mother doesn't know how time passes, and she will only get worse. So visit whenever you want, see her when you can, Your mother is safe, thanks to you, and always remember that. I know that you must love your mother very much, but it might be time for letting go. Just a bit. Peace and love.

Can I ask why relocating her is not possible?
Maybe not this month or next but when you get established in your new job and have a chance to look around your new hometown is there a possibility to transfer her closer to you?
Transferring from one facility to another is not easy, is not inexpensive particularly a long distance. But it is possible.
The facility she is in now may have another near where this new job will take you. If that is the case the two can work together when an opening comes up and helping to arrange the transfer.

You are not abandoning your mom. You are doing what she raised you to do.
You are furthering yourself. Setting yourself up for a better future. That's what all parents want their children to do.
I would almost bet that if your mom was aware of the situation she would tell you to go and pursue this new job.

Thank you everyone for your input - it's given me a lot to think about.
For clarification, I shouldn't have said moving is not an option for her. It could be an option, just one that would be difficult given her health and financial situations and require crossing state lines. But it's not impossible.
I haven't talked to her about this since it's not a done deal by any means, but I believe she would be open to moving. Like my husband and myself, she is not originally from here, and she has lived in many different places in her lifetime.
I think taking the job - which has many advantages for my husband and me - and then later trying to move her closer is the most likely scenario. I do have a local friend who might be willing to check in on her, but if not, I will explore other options.

The question is not move or not move, but how to have your own life while caring for hers? Do what you must to make your life work. Then, do what you can to care for her with the resources you have. If it was me, I'd leave her there until you are settled and then take the necessary time to find a nice place for her near me.

I would not, and stayed here close to my dad, mom, brother, aunt and precious special needs sister to care for them and was with them when they passed. They've all passed now...my dad May 18th and my angel sister Dec 27, 2018. This was my choice, I was their help and support. Now the entire family is gone, and my precious 12 year old German Shepherd is in his last days and I am with him as I was my family. When he is gone I will leave this city/state behind and start fresh elsewhere but I wouldn't take anything for the time I spent caring for my family. This is entirely your choice, no choice is a bad choice. Follow your heart and do what's best for you.