Yes I think it is very normal to feel like this. You are naturally sad and grieving yourself, but feel the need to be there for other family members so are putting a bit of a burden on yourself, while it is going to be a bit of the unknown , how you will actually feel and cope yourself.
Having your clothes set out ready with perhaps some more comfortable shoes to wear if you are driving there, or to be able to slip into after the service. A very simple but useful thing is to think about your breathing at times. As you feel more emotional , or upset, it is easy to begin to breathe in a very shallow way. If you can remind yourself to think about your breathing every few minutes, and to try to breath in more slowly and out even slower. That is something you can do without anyone else noticing, but it helps you to be in control and aware of yourself in those moments. It will of course be a very sad occasion, but seeing friends and family there, wanting to remember your dad well , can also be a comfort and afterwards if you have some tea together or whatever, I think you will find people come up to you and reminisce about times and things that happened when they were with your dad. Hoping that all goes smoothly for you