I think the approach you take to practice would depend on the school of thought you employ. I can provide my suggestions based on the Body School. I can't speak so much to the Round, Traditional, or Square schools. So take my suggestions with a pinch of salt if they don't make sense to you.
My DP and I have very different views - he wants to do the routine repeatedly but I prefer to go through elements to improve technique & therefore the entire appearance & performance of the dancing.
Your DP has a point in that he has to know the routine pretty well in order for you to start doing your job. Without it, his timing, direction, power, and steps will be unclear and that won't give you much to work with. If what he produces isn't clear then you'll probably be equally unclear in what and how to sell it.
It might be an idea to have your DP practice his routines in his head or by himself without you being involved too much. That way when y'all meet to practice the blueprints have already been drawn. The two of you can then just start building. I don't see a reason for you to be too involved if all he's trying to do is learn his routine. In fact, if he's not sure of his routine, he could injure you with an unclear or late lead.
I think that improving technique in one thing often translates into other things, so basics are important.
I'm with you on that 100%. However, is it possible for each of you to work on that separately too? That's what I found works best for us. If each person has good technique, then you can hopefully put the two together and still have good technique as a couple.
Obivously there are times when we need to go through choreography to make sure we are both on the same page but to improve over all, I think we need to work on different aspects. I don't know, may be I am going about things the wrong way. On my own, I tend to work on technique & elements so may be that is where my practice plans come from. I was thinking that one way round this was to ask our coach to give us "home work" to avoid conflict in what we want to do?
Your coach is the best bet to settle the dispute. Of course, coaches are also human, so there is a chance that you will not like his/her ideas. I know I didn't like any of my previous coaches' practice ideas. My current coach gave us a really good practice schedule that suits us perfectly. The good thing about the approach we are following is that practices are test drives of work done off the floor individually. Saves a lot of heart ache and physical/emotional pain by limiting the amount of time together pounding the dance floor.
My advice to you would be to work on yourselves as much as possible and use the time together to make sure that the work you did on yourself contributed to the partnership as a whole. If it doesn't work for the partnership, then my advice would be to find out what it is you can work on individually to make sure it helps the partnership. It's a little scary to do at first but like they say, if you do what you've always done, then you'll get what you've always gotten. From your original post it seems like you're ready to get something different.