You get to decide what you can tolerate in caring for your father. Most people have a line in the sand for what kind of care they can give. For some people, they will care until incontinence of bowl becomes an issue. For others the end of the line might be when the loved one can't transfer with only minimal help. For many caring for someone with dementia, when that person keeps them awake all night every night, that is the trigger to make other care arrangements. Or when the loved one becomes a frequent fall risk.
We all have our limits. You get to decide what your limits are. Can you/are you willing to do this in spite of gagging? Do you think you'll get used to it?
Maybe someone with experience will come along with some tips to minimize the gagging. But always keep in mind that you are caregiving by choice, and it is up to you to determine your own limits.
I never thought I could do it but I got used to helping my mother with her colostomy. For many years she irrigated (an unusual practice now) which meant a huge bag of human manure. Later she switched to regular emptying of bag. She went though a period of leaks. Akkk!!! I used disposable gloves always. I kept a couple smocks on hand to toss over my clothes. There are products you can put in the bag to reduce smells. I also developed an ability to disconnect. I also took a lot of showers.
We all have our limits. You get to decide what your limits are. Can you/are you willing to do this in spite of gagging? Do you think you'll get used to it?
Maybe someone with experience will come along with some tips to minimize the gagging. But always keep in mind that you are caregiving by choice, and it is up to you to determine your own limits.