"like to do" and "like doing" are the same. I think "like doing" is more common. But if you say "I don't like to do that" or "I don't like doing that," it means you don't like it ever. Instead, you can say, "I like sweeping, but I don't feel like sweeping today" or "I like sweeping, but I don't want to sweep today."

Very close! It is grammatically correct but it doesn't properly show your intended meaning. I would say this... I like sweeping/to sweep the floor, but I don't feel like sweeping the floor today. For the first part you can use the infinitive to show the action you like or you can use the gerund (noun with -ing) to show the thing you like or don't like. They mean the same. In the second part, you should use sweeping because you are talking about the thing (the activity) that you don't want to do on this specific day. We always say the activity after I don't feel like.... Good luck. If you have any other questions, let me know. :)