The easiest and quickest way to go to Luoping is actually by train: quite a few leave throughout the day and pass through Luoping on their way to Nanning, Guangzhou and other destinations. The fast trains take about three hours. The cheapest option is the slow train which I once took for only Y 16, but it took 6+ hours as it stops everywhere and waits for lots of other trains to pass. You can buy the tickets at many outlets in KM.
For the journey back remember to note the times posted in Luoping train station when you arrive. Outside peak hours you should always get a ticket, but probably at short notice no assigned seat. Alternatively take a bus, about one every forty minutes. A time-table is here: www.yunnanexplorer.com/transport/station/luoping/

At the train station is a local bus that goes to the main bus station in Luoping, or alternatively take a taxi.

There are hotels in town (as in all Chinese cities), but the town ranks low in the list of attractive towns in Yunnan, so it might be better to stay somewhere closer to the sites.

There are a few main scenic areas, the best known Jinji 金鸡 Golden Chicken. Just north of the road is a village, which had when I stayed there at least one guest house, I think I paid Y20. While nothing fancy, it had the advantage that you can just walk out of the door and you are at the viewpoint in ten minutes for sunrise. Times in Jinji are best at sunrise and sunset.

To get to the Jiulong waterfall 九龙瀑布 catch a minibus going east and change in the next township Banqiao 板桥 for the remaining five km or so. There is an entrance fee for the waterfalls, but I thought they are quite nice.
Best time is during the later morning as you then get the sun on the waterfall, so a good option just to go there after sunrise at Jinji.

South of Luoping is the Duoyihe 多依河 scenic area, a nice river-side walk which has been tarted up with waterwheel constructions from all over the world. There is accommodation down there, I think I paid Y80 during a peak holiday time, there are cheaper guesthouse just on the road opposite to the entrance. To get to Duoyihe take a minibus from next to Luoping's busterminal (right if you are facing the bus station) to Lubuge 鲁布格. That journey takes maybe an hour. If you hire the minibus you can make them stop at viewpoint of the karst mountains somewhere along the way.

April 5 2011 is a main festival day in the area, 三月三, coinciding with Qingming this year, but if you leave it that long there will probably be little left of the rapeseed flower.

According to the website of the Kunming Busterminals, there is a daily bus from KM to Luang Prabang at 18:30: www.km-ky.com/2010/0208/108.html I have seen the bus at the southern bust terminal, so it is running. Timewise it will take about 30 hours and cost some Y400+.

Alternatively, you could catch a bus to Mohan, right on the Lao border, again according to that website a daily sleeper bus. The time table posted in Mohan says that this bus costs Y240.

From Mohan you could cross the border yourself and get onward transport (via minibus) to Luang Namtha, Udomxay and beyond. Or you can catch a bus from Mohan to Vientiane (two busses in the morning, Y200), Luang Prabang (Y100, one bus in the morning), Luang Namtha (3 busses over the day Y25), or the Thai border (billed as Golden Triangle, one morning, one afternoon bus for Y110). All this according to timetable posted in Mohan busstation.

Plenty of cheapo hotels in Mohan should you choose to stay overnight, plus at least one gigantic pink casino-style hotel (used no-doubtable only for legit pursuits) over on the Boten side.

For certain things like olive oil, cold cuts, cheese, pasta and the like try the Box. Yes, the bar on Wenhuaxiang, they also have a food import business that supplies mostly businesses, but they also do retail. They have a long catalogue from which you can order and either pick up in the bar or from 300Y they will deliver. Certain things are in stock at the bar...
I found the Walmart at Xiaoximen totally useless, they do not have anything (or just maybe I have never managed to find it in the cavernous maze. I always think about an earthquake hitting when I am inside that store.)

First of all, I do not think your dad, or anyone in your group would be allowed to drive in China, lacking a local driving permit. So your only option would be to hire a car with driver.

This should be no problem in Dali, but I hope you realize that you will need more than one day from Dali to Yuanyang if you are going through the 'countryside'. Taking the fastest road, i.e. the expressway from Dali to Kunming, then down past Yuxi to Jianshui, then to Gejiu, down to the Red River and up to Yuanyang will take no less than 10 hours, unless you are willing to break the speed limit in some major way. Going on anything other than that road will easily double the driving time.

But with that taken into account, you can certainly do a trip much more interesting than what most people do.
My suggestion for a route would be to drive from Dali to Chuxiong, where you turn south towards Shuangbai and then down to the Red River from there. The main town in that part is Yuanjiang, a relaxed county town. From there smaller roads can take you to Yuanyang, but the most direct route, along the Red River, was blocked between Yuanjiang and Honghe due to a dispute over who pays for a new road. For relaxed travel I would plan at least three days for this route.

Kunming: I had friends here stay at the Yuantong Siji Hotel, opposite Yuantong Temple on Yuantongjie. It was pretty new last year, with kind-of-stylish, if slightly small rooms. Internet in rooms. The rate last year was 288Y per night, no English spoken.

Dali: a good choice in the old town is Rainbow's Nest (?), on Guangwu Road 广武路. If you come from Xiaguan by taxi, go via Boai Lu, turn right (downhill towards the lake) on Yuer Lu and drive two or three blocks, then left. The guesthouse comes after about 50-100m on the right. Just before it is the Caotang guesthouse.
It is a quiet, undeveloped part of old Dali, within easy walking distance to the main streets. Rainbow's Nest, if I remember the name correctly, is a new building, apartment style, some of the (few) rooms come with kitchen(ette), as the original plan was to rent it out on a longer term base. I paid 100Y per night for a very large, very bright suite-style room.

Yuanyang: I have not been for a long time, but I assume the Yunti (cloud ladder) is still the swankiest place in town, with the best rooms and reliable hot water supply. In the off-season, which is March, I do not think you will pay much more than 120Y.