3 Older women likewise are to be reverent in behavior, not slanderers or slaves to much wine. They are to teach what is good, 4 and so train the young women to love their husbands and children, 5 to be self-controlled, pure, working at home, kind, and submissive to their own husbands, that the word of God may not be reviled.
"Does the Bible force older women to work at home?"
No. We know from Proverbs 31 that women have flexibility in the type of work they can do, including work outside of their home (Proverbs 30:13-27). This passage simply opposes the type of idleness that the young widows in 1 Timothy 5:13 were engaged in to exploit the generosity of others.
"It’s oppressive and misogynistic to say a wife must submit to her husband."
There’s nothing misogynistic or oppressive about wives submitting to husbands since scripture doesn’t allow husbands to oppress or exploit their wives (Colossians 3:19). In fact, husbands are commanded to love their wives in a self-sacrificial way, putting her needs and desires above his own (Ephesians 5:25). Wives are commanded to submit to their husband’s authority and husbands are commanded to submit to their wives needs and desires. This creates a relationship of mutual submission where both parties seek to please their partner rather than themselves. When we look at the whole picture and consider God’s instructions for husbands, the argument that submission is oppressive completely falls apart. That’s why critics are always careful to leave it out.