I'd like to put my two cents in here. Long distance relationship punishments can get tricky, but the key that you're looking for is cooperation from your Little to want to follow to tasks. Since you are being met with resistance the first step I recommend you do is to sit down and discuss with them -why- you are assigning the tasks in the first place. Are the tasks health-related and for their well-being? If so, stress that you want them to demonstrate some level of obedience and submission by completing these tasks, but it's also for their own benefit too.
Next, aim to make the task enticing for your brat to -want- to complete. For example: find out if your Little likes stickers. If so, think about having them make a sticker chart together. Optionally there is the Obedience app. (which is free in the app store) which is a BeDeeSeM habit tracker for couples, which is an excellent tool for long distance couples because you'll be able to see their progress AND you can give them rewards as well. These incentives might include: a special video message from you, or streaming a movie together in a Watch2gether room, etc. but something that they desire to do with you. Try to get them motivated to complete your tasks.
If all of those steps have been taken and they still are resistant to submitting and obeying your command then you might want to have a more serious discussion about if they -want- to have a Dominant in their life. Good luck and sending you positive thoughts!