How do I approach my mom about hiring a helper?

avidreader, I would be honest. Reassure her that she isn't being pushed aside just that it is time for a change. You deserve to have a life. Keep saying that in your mind because it sounds like your mom will not be cooperative. Tell her you will be by her side when the helper comes to the house the first few times. Walk her through it all. If your mom flat out refuses or won't cooperate then it'll be tough but this is where you tell her there WILL be changes. If you don't stand your ground you will not be making any changes. So you have to decide how important these changes are for you.
Ok, I've said this several times here but do be very careful who you hire. My mom was all for someone helping her. For my mom it was always about her and this would mean more attention. Well, it was a nightmare for my family. This caregiver, from an agency, became my moms new daughter, taking my place and lawyers got involved. Nobody should say it won't happen to them because it can.
The best of luck to you. You know, you're mom might surprise you and go for it!

Without speaking for your sister, be straight up about it. Suggest hiring a helper b/c there are a lot of things you'd like to do with your life. As long as your sister and you are there to help w/o complaining, there's no need to employ anyone else. She might be stubborn, but necessity is the mother of invention.

It is very common for our parents to resist outside help. It might be best to simply tell her the truth. She needs to understand that it is important for you to go back to work and you would not be as available as you currently are to help her. Even if you do not personally know any elderly who employ outside help - you could reference this site (or use references here and change it to someone you do know of that has had great success with outside sources).

Not knowing your mother's needs; I cannot suggest certain tasks someone could help with and you know what she requires assistance with. I used this with my MIL - she was extremely independent and a perfectionist, but started having much trouble walking and physically unable to maintain her home within the high standards she was accustomed to. After a while, she realized she could use additional help and I mentioned people I did know who were quite pleased with all the outside help they had. I offered and did help her with finding someone. She came to rely on this person and enjoyed her company as well. It is difficult to accept strangers in the home; but we all reach a point where it becomes inevitable; some sooner than others. Good luck and take care.