Does the meaning change without に? I would personally say 当たり前だと思っていた明日が来ること"にも"飽きていた, with に since I see 飽きる being used with に almost all the time. Am I missing something?
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飽きた can take both に and は. E.g.,
mean mostly the same I'm fed up with curry (e.g. due to having had it three days in a row). Possibly は adds contrastive nuance.
For your question, ことも is a version where も replaced は, and ことにも is a version where も is appended to ことに. も is the usual "too, also" particle, suggesting the speaker is bored with the expected things happening over and over again as well as other things.