Mom is angry, any advice?

When she says she want's to go home tell her that she is safe and that you and dad are taking care of her.
Getting dad to go along with some "fabrications" might be difficult since he also has dementia and he is not going to understand the why behind telling mom what she needs to hear to calm her down.
When she asks about her parents and her sister just tell her that they can't be here right now, you can see them later. Or something to that effect without telling her that they are dead. (It is possible that one time you might tell her that they are dead and it will be like she is hearing the news for the first time and it will be upsetting)
Only someone that is cognizant will "know" that they "have not lost all their marbles" she does not "know" how much her brain is NOT working. (maybe this is a good/bad thing about dementia, you don't know what you don't know...if that makes sense)
About the phone number...
Do you have a land line? If so when you are there and she says give me the phone number, give her your cell phone and dial your own number, it will go to voice mail, she can leave a message.

Her wanting to "go home" is called Sundowning and is a very common dementia behavior. The home she wants to go to is her childhood home, the one in her long-term memory, and probably not the home you grew up in. This is why she is insisting that her family members are still alive.

With dementia, one loses their abilities of reason, logic and memory -- and these are all required to handle complex emotions. She can no longer bring herself to a mental and emotional place of peace on her own, therefore telling her "therapeutic fibs" is a perfectly moral and ethical solution. She can no longer "handle the truth", nor can she remember what was explained to her, written down or not (she won't remember to that the written explanation is even there).

You may want to consider meds for her anxiety, if she isn't already on some Many people in facilities require them because of what dementia does to them. Also, for your Dad's sake she needs to be as calm as possible. It is not a failure or evil to consider meds. Many people without dementia take meds in order to function emotionally. And thank goodness for them!

I found this simple list of Rules of Engagement for Rules for Our Loved Ones with Dementia very helpful:

1) Agree, do not argue

2) Divert, do not attempt to reason

3) Distract, do not shame

4) Reassure, do not lecture

5) Reminisce, do not ask “Do you remember…?”

6) Repeat, do not say “I told you”

7) Do what they can do, don’t say “you can’t”

8) Ask, do not demand

9) Encourage, do not condescend

10) Reinforce, never force

My mother did the exact same thing, to the letter, when she was in Memory Care with advanced dementia. She insisted, INSISTED, her parents & siblings were all alive (when they had died decades earlier) and that she wanted their phone numbers to call them, etc. etc. I would NOT tell her 'the truth' b/c it would traumatize her over and over again each time she'd ask me! To tell her they were dead, 1000x a week, what purpose would that serve, exactly? Making 'promises' to a lucid person 20 years ago need to be BROKEN once dementia sets in! So I would tell mom that her mother was living in Florida (we live in Colorado) b/c it was too cold here for such an old woman (heck, grandma would have been 137 years old! :)) I told her that her sister's were on vacation in Italy; that I lost their phone number, that they'd be visiting her next week, and on and on. I had about 100 different 'therapeutic fibs' I'd use depending on the day of the week. The stories would calm mom down and then I'd distract her onto another subject or give her a snack, which she loved.

Sometimes she'd yell OH I KNOW YOU'RE LYING! That would make me smirk, actually, b/c in reality, I'm a bad liar. But hey, this is called Jumping Down the Rabbit Hole 101, in terms of dealing with dementia and all the chaos that ensues. We do what we have to do in the name of keeping them CALM. That's all that matters.

Eventually, when mom's angst and agitation grew to enormous proportions and she was insisting that her mother was at the Memory Care but she 'just couldn't find her', I had the hospice team give her .25 mgs of Ativan which helped her A LOT! Then they increased it to .5 mgs as needed, and that got mom smiling again, thank God, instead of grimacing all afternoon while Sundowning and demanding to go ride the subway to see her parents.

IMO, it always makes a difference what we say and do with a parent who's suffering with dementia. I suggest you read this 33 page booklet (which is a free download) which has THE best information ever about managing dementia and what to expect with an elder who's been diagnosed with it. It helped me an awful lot:

Understanding the Dementia Experience, by Jennifer Ghent-Fuller 
https://www.smashwords.com/books/view/210580

Jennifer is a nurse who worked for many years as an educator and counsellor for people with dementia and their families, as well as others in caring roles. She addresses the emotional and grief issues in the contexts in which they arise for families living with dementia.

The full copy of her book is available here:
https://www.amazon.com/Thoughtful-Dementia-Care-Understanding-Experience/dp/B09WN439CC/ref=sr_1_2?crid=2E7WWE9X5UFXR&keywords=jennifer+ghent+fuller+books&qid=1657468364&sprefix=jennifer+ghent%2Caps%2C631&sr=8-2

She also has published a workbook entitled, “It Isn’t Common Sense: Interacting with People Who Have Memory Loss Due to Dementia.”
https://www.amazon.com/Isnt-Common-Sense-Interacting-Dementia/dp/1481995995/ref=sr_1_4?crid=2E7WWE9X5UFXR&keywords=jennifer+ghent+fuller+books&qid=1657468655&sprefix=jennifer+ghent%2Caps%2C631&sr=8-4

There's a list in that booklet of Do's and Don't's which is pretty awesome, too.

Wishing you the best of luck with a difficult situation. My heart hurts for you and your mom as I know the pain of dealing with dementia first hand. Hugs.

Go along with the delusion as long as it's not harmful to her or anyone else.
When she insists that you give her her mother's phone number, tell her that her mother doesn't have a phone. Or that she got a new phone and you don't have the number yet but you'll give it to her as soon as you get it.
Your mother has as you say, 'lost her marbles'. So being truthful with her about her family being dead is only going to hurt her. Go along with her nonsense if it keeps her calm.

Conversate with her and go along with whatever she says. I still remember a physical therapist from daycare calling me asking to speak to my grandma who was refusing to stand from her wheelchair. Per my 89 yr old grandma her father had spent way too much money on the wheelchair therefore there was no way she was going to let the strange lady take it away and steal if from her, her dad would be too upset. To agree with them calms them down at times, I think it provides comfort to them. At times I would talk to her like a child and say her dad and/or brother's were working and would come home soon, I would ask her questions about them try to drift her worries away while still keeping her long lost loved ones present. It's not easy, but worse is to try to argue with them.