To write your example correctly in formal English, you would require two possessives: one for the primary adjective and one for the identifying name in apposition: “I liked my husband’s, Steve’s, hawk.” Otherwise, without punctuated apposition, you would have a restrictive modifier that suggests you have more than one husband (e.g., The hawk is my husband Steve’s and not my husband John’s).

To avoid this awkward construction, you could re-write the sentence in another way such as:

I liked my husband’s hawk.
I liked Steve’s hawk.
My husband, Steve, had a hawk; I liked it.

As the post states, “When an appositive is essential to the meaning of the noun it belongs to, don’t use commas. When the noun preceding the appositive provides sufficient identification on its own, use commas around the appositive.” Since John is my “favorite” cousin, we know that he is not the only cousin. Therefore, the name John is essential to the meaning of the noun “cousin,” and no commas are used. See our posts Essential, but Is It Important? and Commas with Nonessential Elements for rules on commas with essential and nonessential clauses.

We recommend using a comma after “humorousness.”

Your examples do not contain appositives. Our Rule 6b of Commas says, “Use commas to set off expressions that interrupt the sentence flow (nevertheless, after all, by the way, on the other hand, however, etc.).” Therefore, the following are correct:
I said I would do it, and as you may recall, your brother heard me.
Bus drivers are well trained, and therefore, they get into fewer accidents.
Joshua and Caleb had brought back the minority report after spying out the land, and as a result, they were spared the judgment against the unbelieving Israelites.

Where should the commas be in the following sentences, and why?

e.g. I said I would do it and, as you may recall, your brother heard me.
e.g. Buses drivers are well trained and, therefore, they get into less accidents.

e.g. Joshua and Caleb had brought back the minority report after spying out the land, and as a result they were spared the judgement against the unbelieving Israelites.

Thanks.

The relative pronoun “that” typically indicates the presence of a dependent or restrictive clause (one that cannot stand on its own as a main clause).

Example:
This is the book that he put on the table.

The “that” clause identifies a specific book.

In the examples that you cite, there is a full dependent clause functioning as a noun subject or object in apposition to another noun subject or object already named. In these cases, the dependent noun clause acting in apposition to the subject or object noun would be set off by commas:

The problem [subject], that you did not pick up the packages [appositive renaming the subject], delays the entire production schedule.
I think the solution [direct object], that he hired a replacement [appositive renaming the object], was the best course of action at the time.

At the same time, both sentences could potentially benefit from revision:

Because you did not pick up the packages, the entire production schedule is delayed. (The problem is apparent.)
I think his solution to hire a replacement was the best course of action at the time.

We recommend writing as follows:
Restrictive appositive (the topic): My manager created the discussion topic “What concerns do you have at work?” in my appraisal document.
Nonrestrictive appositive (a topic): My manager created a discussion topic, “What concerns do you have at work?”, in my appraisal document.