The reaction of the target to the dream is up to the target
The normal version of dream merely states:
If the target is asleep, the messenger appears in the target’s dreams and can converse with the target as long as it remains asleep, through the duration of the spell.
Nothing there states that the messenger has any control over the target, and normally if a spell allows you to control another creature, like suggestion does, it will explicitly tell you so, and will tell you the limitations of that control, too. Dream certainly does not allow you to cast additional spells on the target in the dream.
The only way you could possibly influence the target here is as you would be able to in a normal conversation: you can try to intimidate it, persuade it, or deceive it into disclosing information. How such attempts are handled would follow the normal rules of resolving social interactions.
The ability to create an environment that may feel threatening might give you circumstantial advantage on those attempts, at the DMs option. The spell gives no further information on what "landscapes, objects and other images" encompasses, so the DM must rule if they can have someone dream they directly are affected by the environment, like bound to a chair, or feeling the heat of glowing irons.
Given that the overall experience is described as a conversation, and given that there is an explicit alternative option for instilling nightmares, I would rule it cannot be anything too horrific, and would not include things like restricting, suffocation or causing pain.
The "nightmare" section of dream reads:
You can make the messenger appear monstrous and terrifying to the target. If you do, the messenger can deliver a message of no more than ten words and then the target must make a Wisdom saving throw. On a failed save, echoes of the phantasmal monstrosity spawn a nightmare that lasts the duration of the target’s sleep and prevents the target from gaining any benefit from that rest. In addition, when the target wakes up, it takes 3d6 psychic damage.
Even this does not allow you to control the target to disclose a secret. You merely can deliver a message of up to 10 words, there is no conversation here. The target then makes a saving throw and suffers damage and loss of rest if it fails. That's it.
Anything beyond these two functions, conversation and nightmare, would be DM ruling.