(You seem to get the answer, but I already wrote my reply, so I posted it.)
I know you often use Jisho.org, so I confirmed that the site had the entry of 含める before posting my previous reply. That's why I wrote "Did you check in your dictionary if the verb you thought the potential form was really the potential form?". Anyway, as nice gaijin-san linked, 含める is actually not the potential form of 含む but an ichidan verb, meaning "to include" here.
含む vs. 含める is a special/exceptional pair of verbs, so your confusion is understandable in a sense. When it means "to include", they are both transitive, but the former is non-volitional and the latter is volitional.
アジアはオーストラリアを含む/含んでいる。
Asia includes Australia.
FIFAはオーストラリアをアジアに含めた。
FIFA included Australia in Asia.
As you can see in the examples above, the subject of 含む(= Asia) is the one that includes the object(= Australia), so it's close to intransitive verb in this sense. On the other hand, the subject of 含める is the agent (= FIFA), and Asia is indicated by に. Australia is the object in both sentences, so を is attached to it. (Incidentally, the passive version オーストラリアはアジアに含まれる/含まれている is often preferred for the first one.)
含む can be volitional when it means "to hold something in~", so 含める can be the potential form of 含む in this meaning.
e.g.
この果物は大きいが、小さく切れば赤ちゃんでも口に含める。
Was it the past tense of 持てる which was also the potential form of 持つ?
Yes, もてた is the past potential form of 持つ there. While とても活気のある話し合いを持った is just a neutral description of a past event, 持てた implies the subject's/speaker's satisfaction. Thus, this potential form only can be used in positive meanings. You can't say, for example, とてもひどい話し合いが持てた (well, except as a sarcastic expression or something). It's the same as "we were able to have a good meeting" in English, no?
a REGULAR conjunctive form should be used if the sentence does not end there. And a conjunctive form of other conjugation such as that of potential form never plays in such role.
That's not correct. The potential form, passive form, causative form etc. of a verb works as a verb, so the -masu stem of these conjunction forms can be used to connect clauses as same as the regular/original verb's stem.
e.g.
彼は荷物を持ち、旅に出た。
彼は重い荷物が持て、その上どこまでも歩ける。(potential)
彼は知らない人に荷物を持たれ、不安になった。(passive (of adversity))
彼は友達に重い荷物を持たせ、自分は何も持たなかった。(causative)
彼は重い荷物を持たされ、疲れ果ててしまった。(causative passive)