Shunshoku Umegoyomi Vol. 1: The Yōshi

Fig. 1: 私き
やア今日帰
ると直に住
けへをねが
つて。

Yonehachi finishes her monologue (finally):

"If I return [home] today, I'll immediately ask [permission] to change houses (fig. 1)."

「私き」 is an alternate form of the modern 「 私」 that we've encountered before (see fig. 3).

Fig. 2: 婦多
川へでも行
て辛抱して
おまはんの
身を少しも
樂にさせ申
てねへヱ
トしんじつ
見へし女の
いぢ男はし
ゞうふさい
でゐる

「けへる」 is clearly an alternate form of 「帰（かえ）る」. This also helps to explain 「住けへ」— it's just 「住み替える」, or "to change one's residence". 「ねがつて」 is of course 「願って」— "to desire".

"Even if we [have to] go to Futagawa or somewhere, I will endure it if it makes things a little more comfortable for your body [health], OK?" the woman [Yonehachi] said, and showed her true obstinacy, [at which] the man [Tanjirou] continued to keep [his mouth] shut (fig. 2).

First of all, we encounter the place name Futagawa （婦多川）. As explained here, it is just another name for Fukagawa （深川）, which is itself a former ward of the old Tōkyō City. It can be found in the modern day ward of Kōtō ward, which is made up of Fukagawa and Jōtō, another former Tōkyō City ward.

We see the odd calligraphed form of 「身」 from last time (see fig. 4) again here. Note how this time it has the reading 「み」, which made it quite easy to determine which kanji it was.

I wasn't entirely sure about how to transcribe the part I've got as 「させまして」, particularly the 「まし」. I couldn't think of anything else that made grammatical sense, but it seems like there might not be enough space for a 「し」. Edit: as Matt has suggested in the comments below, what I thought was 「まし」 is likely the kanji 「申」. The meaning is unaffected by this change, but the reading would be 「させもうして」.

In the togaki (see fig. 5), we see 「見へし」. This is the shimo-nidan "ya"  verb 「見ゆ」 in the continuative form （見へ） followed by the auxiliary verb 「き」 in the attributive form （連体形）. The auxiliary verb 「き」 has an irregular conjugation, in which the attributive form is 「し」. It is used to indicate personal past or recollection （体験回想）.

I wasn't entirely sure about the kana 「く」 in the left column of the togaki. However, nothing else fit the context, and 「久」 had the closest-looking kuzushiji form of all the parent kanji for 「く」.

「ふさいで」 is derived from the verb 「塞（ふさ）ぐ／鬱（ふさ）ぐ」, which means "to feel depressed", or "to mope".

Edit: as suggested by Matt in the comments below, what I read as 「ご」 is more likely 「ゞ」, meaning that 「しゞう」 (which would be read as 「しじゅう」 in modern Japanese) is most likely 「始終」, meaning "continuously" or (more literally) "from start to finish". This would then suggest that the meaning of 「塞ぐ」 is likely an alternate one — "to shut up" or "to close (one's mouth)".

Fig. 3: よね
「ヱモシそ
して養子
に

"Huh, then as for the house that adopted you as a son-in-law, well (fig. 3), why was it that its fortune suddenly collapsed, huh?" Yonehachi asked (fig. 4).

I wasn't entirely sure about the beginning of fig. 3 (the 「ヱモシ」 part), so if that looks wrong, let me know.

Fig. 4: ど
うした訳
で急に身
代がたゝ
なくなつ
たのであ
りますヱ

In fig. 3, we also see the term 「養子（ようし）」, which refers to an adopted son-in-law. As explained in this book, the yōshi system of adoption came into play in those families who wanted to prevent the extinction of their family name/lineage, or those families who felt their biological sons did not possess the competence necessary to adequately preserve and propagate that legacy. In such situations, a suitable man would be adopted into the family by having one of the family's daughters marry him. He would change his last name to that of his adoptive family, move into that family's house, and be removed from the koseki （戸籍）, or family registry, of his old family and added to that of his new family (this was essentially the same process regularly followed by women when they married into their husband's family). Individual yōshi might have risen from poor backgrounds to a place of sufficient prominence in society, or they might be sons from wealthy families who were not the firstborn, and thus had no responsibility (or right) to their own family's legacy.