Mom nearly died from C. diff last year, and my sister has it now. Do we tell mom?

In answer to your question: I would avoid letting mom know, if possible. If sis will make a full recovery, why drag up horrible feelings for Mom? And I say this as someone who is pretty blunt and "tough love" in general. But the worry about health gets so extreme as people get older, I've learned to not spell things out unless they are absolutely necessary. I think, from your post, you already know she's too fragile right now to hear this, even though your sister will be fine.

Are you familiar with fecal transplant. You can google it. Much research in about 5 years ago showed it to be instantly effective against C-diff. Unfortunately the combination of "the thought of it all" and one or two incidents of transfer of problems one person to another almost stopped it. There are still some gastroenterologists who are doing this; being SF and a place where there are many auto-immune problems, there are many who actually now have done this in a do-it-yourself manner.
I have seen MANY deaths from C-diff and people underestimate the number. Usually listed as complication of auto-immune or complications of cancer treatment, or whatever, it is missed that this is DEADLY. We are not talking diarrhea here, but rather explosive propulsive emptying of the body continuously, and inability to hold any nutrition, and wasting of the body.
There is no reason not to tell Mom Sister is dealing with this. Hopefully she will be one of those cured by medications. This is like any disease; would you withhold information about most diseases? Only you know Mom, her reactions to things, her worry and etc. You are the best judge of telling, or when to tell. Trust your own instincts.
I will tell you frankly, if sister isn't helped by the more comment "treatments", you need to explore fecal transplant. Research it online.

You don’t get c. diff from antibiotics. It’s what’s left around when antibiotics can’t clear it.

Years back, I discovered I had a latent infection called MRSA. I told my sister who is a doc, and she said I was still clear to see my parents. In this situation, check with your doc to make sure you are not actively contagious. If you’re not, I wouldn’t bring it up to mom.

My mom gets anxious over challenges her children or grandchildren are going through too. We don’t lie to her but we do often omit things or just not mention at all if we can get away with it, telling her after the fact. When my son got COVID around Christmas we just didn’t say anything since we weren’t getting together anyway and I have never told her about it because it was a fairly mild case and all recovered, why make her worry. My brothers kids and wife got it earlier on and she was torn up about it for weeks. I have had some medical issues lately and while I tell her I’m not feeling great or that I am having surgery I minimize some of what I’m going through so she doesn’t fret. I can do this because I don’t live close by and only see her via the Show so I can generally “showtime” for her.

My point being that if I were in your situation with my mom I would probably let her know sister isn’t feeling well and probably has the flu they aren’t sure but they know it’s not COVID, something like that so sister can lay low recovering and Mom isn’t stressed that she isn’t hearing from her or something. Unless of course your sisters condition gets to the point of hospitalization in which case reevaluate, I might tell mom she is in the hospital where they can better treat her but not that they know it’s C-diff since that holds a particular fear for her until and unless you absolutely have to. C-diff doesn’t always require a hospital stay, in fact it usually doesn’t we just hear more about those cases for obvious reasons so don’t get overly worried yourself either, your mom will likely pick up on that as well. Hope your sister is better soon (tell her to eat fermented foods) and you and your mom don’t suffer too much from Moms anxiety over it.

When my mom reached the age of 88 and became quite anxious about everything, I told my brothers that our rule of thumb should be not to tell mom any "story" that didn't have a happy ending.

We no longer said "grandchild is being tested for...", or "In two weeks, sibling is going to have surgery for...".

We told her happy endings only.

I wouldn’t. How would it benefit Mom in any way? Would just upset and worry her.

My aunt 93 suffers greatly emotionally when someone shares bad news about family members. She doesn't sleep and quits eating. She has major anxiety and frets over everything. She also has advanced dementia.

I have recently had a mini stroke but found some serious cardiac issues while in the hospital. I refuse to tell her anything until all procedures are over and I am well. I am one of her several caregivers. Its not worth upsetting her.

What possible good can come from telling her? Leave well enough alone. You both have enough to deal with. Why add to the pile?

Why does your mother need to know? Does your sister live somewhere else so she is not visiting your mother right now? If your sister's treatment is goes well and she recovers at home, there does not seem any point in worrying your mother. A lot of sharing can be kept to a "need to know" basis.

I used to be all for 100% honesty. But, I have also come to value the saying "silence is golden" 😶

My DH has shown me that sometimes a little minimising ie "watering down' or delay is necessary. For kindness. (He calls it anxiety minimising strategy).

Just as Barb & Llama said, the happy ending approach. No "there was a great flood!" until "There was a great flood but everyone was saved!". Or even "There was a great flood, the people were so brave, nearly everyone was saved. They are rebuilding".

Like a news reporter, it's all in the delivery