How does one not feel guilty when deciding to put mom in a home?

There must be something wrong with me. Guilt was not an emotion I felt when my mom went into a nursing home.

I felt great sadness that she had broken her hip, had CHF and dementia. I felt regret that she hadn't been granted a quick and painless death. I knew that she never wanted to be a burden to her children: we were running around like chickens, trying to do the right thing and I think we made every conceivable mistake.

Guilt? I did nothing wrong. I had a mortgage to pay and a new grandchild to help with. I had a career that needed to continue if I was going to be able to retire. My husband had just finished 3.5 years of being unemployed and his health, mental and physical was my number one priority.

Grief maybe, but not guilt. Guilt is for folks with malice in their hearts.

You have to realize the realities of the modern day, and the inevitability of placement if parents live to be that old.

Apply for Medicaid to pay for it. Do not use a cent of your own money to pay for her care.

So you feel guilty about what your caregiving is doing to your marriage, and guilty if you place her in a care facility. It's either one or the other (I'm being facetious). Isn't it amazing that those who make sacrifices in their own life for others, still are riddled with guilt. You've cared for your mom for 4 years now at the expense of ruining your marriage. Take credit for what you've done and how you've cared, and erase the false guilt you impose on yourself.

Begin a Medicaid application for your mom. When you say “home”, do you mean assisted living, memory care or nursing home (some of which have MC units)? If an ALF or MC, Medicaid won't cover room and board. In a nursing home, Medicaid will cover nursing care and room and board. Once your application is submitted but not yet approved, look for a facility that will accept “Medicaid pending” patients. This allows your mom to be admitted into the facility while her application is awaiting Medicaid approval. She will owe nothing during that time and the facility will be paid nothing during that time, which will be several months. When she is approved, the facility will be paid retroactively.  You may want to visit a Medicaid attorney to fill out your application.

I don't know how you avoid the guilt, I think it may be a natural part of it you have to accept but not let overwhelm you
We can tell you you shouldn't (because you shouldn't) feel guilt but we all do I think. If you care about someone, there is guilt in putting them in a home.
You get one life though, and you need to do this for you,
How to lessen the guilt would be to find the best home, let her have input into looking for homes and try to make her see that in some ways, it will be better for her. You do the best for her, as you have already been doing, but now you do the best for her and you as well.
Once she is settled and things are going smoothly the guilt will lift and you will be happier. You will see you have done the right thing. It will pass.

Your Mom will have to apply for medicaid when her savings are sufficiently spent down. I would say, as to your guilt, that you are not a felon. You are not a criminal out there doing evil things and taking pleasure from the misery you cause. That is the place where guilt belongs.
There is another G word for you. That is grief. You are grieving that you cannot go on, that you are drained, that you are not a Saint, but a human being and you are beaten down by your limitations. That is worth tears. That is worth your grief. And that is what you are feeling.
Speak with your Mom's Doctors and tell them that you cannot go on now. Find guidance for application for medicaid in your state. Begin to explore options for placement.
Forum has a timeline on top. Go to care topics and look up those that interest you, and begin to read and gather information. I have learned SO much on this site.
Do also consider that we are close to getting our elders vaccinated in nursing homes, but until that is done, if you can hang on a bit, and begin to slowly explore options, google medicaid and learn about things, you can perhaps wait a bit for Covid 19 to be in more control. Right now it is difficult even to visit facilities, and at 98 your Mom would be terribly vulnerable to the virus.

98 years old! Wow. Is she alert, does she understand what is going on?
If she does, talk to her about placing her in a home where they can tend to her needs, etc. Tell her you or family member will visit every day and bring her some sweets or whatever it is she likes.

Go check out several nursing homes to find one you fill comfortable with. If she has no money, you will have to apply for Medicaid and you will need to make sure the nursing home you select for her takes medicaid. It's a long application and she must spend most of what she has left on the monthly charge at the nursing home. The nursing home will help you with the medicaid application.

Good luck.