Wilson: It looks like you have a very good starting list for your vacation. Starting from Lyons, CO I definitley recommend a trip thorugh Rocky Mtn National Park (if you have not done so), lots of small streams and lakes and camping opportunities. As you go west from Estes Park, CO over trail ridge road, the road T's into hwy 40, if you took a right and go about 5 miles then take another right on hwy 125. That heads to Walden, CO. Just before you get to Walden the road does a 90 degree right turn, at that point hwy 12 heads west. If you like to fish lakes, the Delaney Buttes Lakes are about 12 miles out on hwy 12......very nice fishing and has camping but very few trees for shelter. Fishing can be done from shore but a belly boat or pontoon will get the most action. There is a very nice place to eat in Walden called the River Rock cafe. Heading north out of Walden, CO the road T's about 13 miles north, if you take the left fork that will put you on hwy 125 (turns into hwy 230 at the WY border). Walden is called the North Park area and is the head waters for the North Platte river. As you travel west/north on hwy 125 you will see a number of public access points to fish the North Platte, they are all on the right side of the road. The first one will be about six miles from the junction and offers a trail into the North Park Canyon area (no camping). Further down you will need to pay close attention as the signs can be easily missed. Look for the 6 mile gap access point, turn off the hwy, it is dirt road and about a two mile drive to the access point, there are camping spots here and the access point is a great point to start exploring the North Platte. Further along on hwy 230 you will see the Douglas Creek Confluence access and the French Creek access points. Both offer camping and good access to fishing, but don't go into Douglas is it has been raining as the road can get slick and difficult to climb the hill going back to the hwy. Hwy 230 runs into Riverside, there is a nice bar called the Mangy Moose that cooks awesome hamburgers and there is a nice diner right next to the bar and across the street is the Lazy Acres Campground right on the Encampment River. Heading north out of Riverside the road turns into hwy 130, keep an eye out for the Treasure Island access point (on the right), it offers some very nice fishing on the island (about a mile of public access, no camping). Hwy 230 heads into Saratoga. If you get a chance stop for dinner at the Wolf Hotel, they offer a fantastic meal. Saratoga also has a hot springs which the family would enjoy and Saratoga Lake on the north end of town can offer some exxcellent fishing. Before I forget, about 10 miles before you get to Saratoga there is a paved road to the right (also called hwy 130) that heads to Laramie, well worth taking to the top of the Snowies, the views are awesome and there are some excellent fishing in this area, I like Frensh Creek and Douglas Creek, it requires some hiking but the effort will be well rewarded.
Going North out of Saratoga you will see a couple more access points to the North Platte and the road T's into Hwy 80, if you go west to Sinclair and then take hwy 351 north you will go over a mountain range and see a couple of large resevoirs on the right about 40 miles from the hwy the road crosses the North Platte, this is the section they call the Miracle Mile, it isn't what it used to be in it's hay day but still is fun to fish (it is a tailwater) and the land is all BLM so there is access on both sides of the river and lots of camping areas. If you follow the dirt road north it will take you through fremont canyon and eventually to the Grey Reef section of the North Platte. There is primitive camping at the dam. There is a fly shop at the dam, get a North Platte access map, it will detail all of the public access points along the river, all the way to Casper. The Grey Reef is also a tailwater and can be technical fishing but the rewards can be awesome.
Wilson: Yes, I live in Laramie, WY so that is my home fishing area. If you decide to go that direction, I can also point out a few other spots (just PM me as you get closer to your trip). As you travel north you might also consider Yellowstone NP if you have never viewed the park. It has some great fishing and also gives the family something to do and it is well worth the detour, you just have to expect the crowds on the road, but there are plenty of streams and lakes so you don't have to fish in crowded conditions.
I tried fishing the Koshka river in the Bitterroot last year and didn't have any success at all. I still don't know whether it's because I was trying to use southwest angling flies and techniques that may not work there, or because there's no fish!
The latter is a possibility, because I also was fishing the Salmon river in Stanley Idaho, catching nothing but 4" trout, until a local came up and said, don't bother, there's nothing bigger in that river.
The only moderate success I had in Idaho was in some small creeks in the Sawtooths, where I was able to have fun catching 6-8" fish. Still don't know whether they were brooks or the so called "bull trout."
If any Idahoans here could shed some light on the matter of fishing those rivers, I'd like to hear.