Today, I returned from work early. My stomach still hurts. Tomorrow, we should go dig outside, but probably won't be able to.
Simple is good. I think there are only two errors, and one of them might not really be an error.しごと から はやい かえりました should be 仕事から早く（はやく）帰りました。そと で 堀に行く べき です should be 外で掘りに行くべきです。 The 掘り is the ～ます form of the verb 掘る with the ます dropped, so I'm pretty sure you need the hiragana ending there. However, it is acceptable under some circumstances to write ほり as 堀, and I'm not 100% sure which those are.One last thing: I find the です in the middle of the last sentence jars, and would like to replace that comma with a period. I'm not sure if this an error or not, or even if my impression is something a native speaker would agree with.
Why is it 早く and not a -て form or something?
Why? Jeez, I dunno.Well, if I were to hazard an explanation (and it is hazardous), I'd say that 早い here is acting as an adverb.Come to think of it, you could say 早くて帰りました... I think... Not absolutely sure that's right though.There are certain verbs and phrases that take ～て forms: ～ている ～てください ～てみる ～ておく（～とく）, but if you just apply it to any old verb what usually happens is a kind of conjunction-- first you do/did this （～て）, and then that （～る）. Some of the idomatic forms I listed above could be translated, with some squinting, that way, e.g. してください "Do it and give to me." -> "Do it for me." -> "Do it please." Or してみる "Do it and see."