I started typing as @pinkdelightwas posting but I agree with her questions.
Take the dogs and daughter and partner out of the picture for the minute and focus on the key issue. The key issue is that your rural house doesn’t work for you and the place in town is better.
Now build up from there. Practical questions first: are you eligible for this house as two people (mum and daughter) or is it only offered to a family of three?
If you are eligible as the two of you, I would prioritise the move for the reasons above. You need your independence back.
So right now, assuming you need to take up the exchange before a deadline, I would take it. I would explain to partner that DD is coming and so does her dog. What happens then depends…
Do you ever see your daughter moving out? That’s not a conversation you can have right now as it will look like you’re choosing partner over her. But she’s 28, does she work, if not will being in town make it easier to find a job she can walk to?
How is your relationship with DP outside of this disagreement - what do you mean that DP is showing true colours?? Are there other problems in the relationship? Would they find work easier in town (more options) and would life be better if they worked? Have they ever worked when you’ve been together and was life better then?
The house exchange is throwing all of these questions into sharp relief so it’s a catalyst for some difficult decisions.