You don't have to convince your sister. You have to convince yourself, set your boundaries and stick with them. I'm not sure what your concern actually is. Do you feel guilty saying no? Do you feel sad because you wish you could spend this time with her but know you can't because of lack of money and need for more of a schedule?
I suggest that the first thing that will help is for you to decided what it is that you want and can afford/manage. Then tell your sister. If you don't want to have a discussion about your choices then tell her in a nice way that this is the way it is for now and that talking won't change your mind.
Be warm and friendly. Let her know that you do want to spend some time with her; that you love her and her kids, etc. But that you have to do what is best for you and your family. Don't try to convince her that you're right. This is just the way it is. The two families have different income levels and different needs.
There are many things in our area that are free or have a nominal fee. I don't now how large Angola is but hopefully you can do things together at very little cost. If gas money is a problem for you but not for her, perhaps she could pick you up? Does she have a large enough car? Do talk with her about planning things that you can afford. Parks, swim pools, Parks and Recreation activities.
About being back home for nap and bedtime. Can you make an exception one day in a week and perhaps twice in a month. You don't say how old your child is. My family has often been out all day and the babies nap in their stroller or on a blanket in the park. You may benefit from getting out of your comfort zone from time to time. Doing so will benefit your child too. Too much needing to stick to the tried and true stifles growth.
I suggest that you decide what you want, find a way to feel comfortable with your decision, relax and do what is fun. Tell your sister, if she continues to rag, that takes the fun out of the time you do have together and ask her to stop. IF she doesn't, you may have to stay away from her for awhile. Don't listen to her reasons for doing what she wants if you've found that they don't work out. Say no and stop the conversation.
You are responsible for your happiness and she for hers. Work on finding ways to compromise and have a good time together. Be assertive. Be direct. Be kind. Be loving.