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Maybe after that week your mom doesn't want you talking to her is up, you can communicate your feelings to your sister. Let her know you don't want her to move back but you do want to keep in touch with her without her getting worried. Ask her if maybe the two of you can set up at least some time per week where the two of you can talk. For example, maybe if she's free on Saturdays, the two of you can set aside some time that day where the two of you can talk each week. It may help to at least have a set time to talk.

For a while, my sister moved up to a place in New York that was right by the Canadian border. We also wrote each other letters. Letters are a good way to keep in touch because you can write one to keep her informed of what's going on in your life, and when she has some time in between classes or on a free day, she can keep you updated as well.

It may also help for you to get out more so you don't have as much time to dwell on things. Maybe join clubs and activities or hang out more with friends, for example. Of course you'll still miss her some and that's normal, but it may help to get your mind off of her for a little while.