As I suggested in During the "Viking Age", how common was it for Danes, Swedes and Norwegians to become vikingr? Was this something many people did, or just a small group? What was the social class of the people who went? How did normal farmers in their society see them?, If your father was away from home due to the Viking Age expedition, then your family probably primarily belonged to the local magnates or the military retinue who served the former as their lord, not the ordinary farmer.

The following is basically a cut and paste from some my previous posts on the relevant question, such as How did pre-modern Scandinavians maintain their sanity throughout the long winters?

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As for the education of the young elites in the Viking Age Scandinavia, the closest (or almost only) account we have is a stanza of the poem by Earl Rognvald Kali of Orkney (d. 1158) in the northern frontier of the British Isles (and settled by Norsemen), well-known as 'the Nine Arts of the Vikings'. The poet lived in the first half of the 12th century, but some of the 'arts' boasted here by him are said to date further back to the Viking Age (usually dated from ca. 800-1050).

'At nine skills I challenge -
a champion at chess:
runes I rarely spoil:
I read books and write:
I'm skilled at skiing:
and shooting and sculling
and more! I've mastered
music and verse'.

Quoted from: Hermann Pálsson & Paul Edwards (trans.), Orkneyinga Saga: The History of the Earls of Orkney, Harmondsworth: Penguin, 1981, Chap. 58 (p. 108.)

Rognvald Kali is said to left his home in Norway (He was half-Norwegian and half Orcadian) first at age 15 in saga, but the scribe of the saga does not add further information how he learned these skills in his home, unfortunately.
So, we unfortunately don't have the reliable contemporary evidence on 'how structured' part of OP's question.

The following paragraphs are complements to some arts mentioned in the poem:

• Chess: the provenance of the very famous Lewis Chessmen found in the Western Isles of Scotland is generally ascribed to the workshop of Trondheim, Norway, established as an archbishopric in the middle of the 12th century. In addition to chess, however, the Norsemen knew another table game, called hnefatafl. The Vikings seemed to bring the practice of this table game with them. This 10th century hnefatafl, found in Ballinderry, Ireland, is thought to be manufactured in the Norsemen-settled Dublin. This gambling dice (blog in Norwegian) is also found from Late Medieval Bergen, Norway.
• Reading/ Transcribing: Don't you remember the medieval sagas from Iceland, allegedly telling the deeds of their ancestors? Iceland and some Atlantic Islands settled by the Norsemen have traditionally said to enjoy relatively high degree of lay literacy in the Middle Ages. Some of highly literate medieval Icelandic magnates like Snorri Sturluson almost certainly had some private book collections and let them read for them. Even an authority of Icelandic literature in the middle of the 20th century claimed that to transcribe manuscripts was a kinda passtime for medieval lay Icelanders during winter, but this hypothesis have been almost dismissed later. Post-Reformation Icelanders was known to be enjoying to hear sagas read around (sagnakemmtun) in the family gathering in winter night (kvöldvaka) (Driscoll 1997: 38ff.), but I'm not sure whether this tradition can date back to pre-Reformation Medieval period. AFAIK its first verified evidence at least could only date back to the 18th century.
• Skiing: with the rivers frozen and snows covered in the ground, skis and sledges were not just pastime hobby, but also very useful for traveling. The winter assembly/ market, Disting (disating) in Uppsala was said to be held in the middle of winter when the traveling by ski/ sledges were most easy, and the Birkebeiner, the political faction in 12th and 13th century Norwegian Civil War is famous for their employment of skiing, as shown in this 19th century painting, taken an anecdote of the infant (future) King Håkon IV of Norway (r. 1217-63) rescued by the two warriors carrying him across the mountains during winter, as a motif.

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On the other hand, I suppose you can play some outdoor toys and sports also during the summer. I wonder whether you and your sibling could enjoy playing with this kind of wooden toy, found in the abandoned medieval well in Norway a few years ago , also in your house if your parents or their servants were so generous to make it and to present to you, together with some bucket......

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Works mentioned:

Driscoll, Matthew J. The Unwashed Children of Eve: The Production, Dissemination and Reception of Popular Literature in Post-Reformation Iceland. Enfield Lock: Hisalik, 1997.