The serialized version was cancelled. This is an independent version that the artist is doing as a passion project. We are working with them directly to provide an English version, which is available on pixiv.
The translation is correct. Kotone's assumption that it was the son was wrong and Momo was right when she said the father. Kotone thinks Momo is crying from the joy of being right for once.
The artist is continuing it independently and we're working with them to provide and English version. The chapters are uploaded:
https://www.pixiv.net/en/users/122109038
Chapter 3 was not released until this past Friday in Japan. They mentioned on their Twitter that they were going to be updating it more frequently, hence the end note.
The artist is continuing the series independently, and I will go past where the official serialization ended. We're working with them to provide an English version on Pixiv.
https://www.pixiv.net/en/users/122109038