help with Hokkaido itinerary

My brother will be going to Kitashinano, Chitose City, Hokkaido this July and I would like to plan a 3-day simple itinerary as well. The things I wish to do in Hokkaido are:
1. Otaru Music Box Museum
2. Kitaichi Glass
3. horse back riding in forest trail if possible
4. best lavender fields in bloom

Any suggestions? Any help is appreciated, especially on getting around. The last I've been to Japan was back in 2009 so I can't remember that much about transportation. Thank you!

Kitaichi Glass and the Music Box Museum are not too far apart. From Chitose you can just take a train, most transfer in Sapporo but some go straight through to Otaru, and walk down toward the canal and turn right 1 street before the canal street through the main historic district until you get to the steam clock at a major intersection which is the Music Box Museum.
Kitaichi Glass location:
https://www.google.co.jp/maps/place/%E5%8C%97%E4%B8%80%E3%83%B4%E3%82%...

Music Box Museum:
https://www.google.co.jp/maps/place/%E5%B0%8F%E6%A8%BD%E3%82%AA%E3%83%...

The lavender fields are near Furano, NE of Chitose. You can take a train to Furano and a train to the fields, but it would be easiest to rent a car. Lots of information on this site:
http://www.japan-guide.com/e/e6826.html

My only horse experience in Hokkaido has been in Shizunai but not for riding. This site may give you some ideas:
http://en.visit-hokkaido.jp/activities/horseRiding.html

Thank you very much! If you only had a 3-day trip, how would you arrange it? And are the lavender fields in full bloom? The horse park I picked was the Northern K? Park? Is that nearby as well?

If you had 3 full days, I would probably arrange it something like this in any order as you're using Chitose as a base:
Day 1: Morning: Otaru - glass and music boxes as well as the old town on the way.
Afternoon: Catch a bus from in front of Otaru Station over to Shukutsu to see the Aoyama Villa, an old mansion from the herring fishing days (that has a convention center built behind it that serves as the entrance). You could then walk down to the "Nishin Goten," the old style fishing offices where the workers lived downstairs and the owners lived upstairs.
Bus back to Otaru and train(s) back to Chitose.

Day 2: Train to Furano and local train to Lavender Batake Station and a walk to Farm Tomita to see their flowers. You can then get a local up to Kamifurano Station ("Upper Furano") and take a taxi to Flower Land Kamifurano. The walk back is downhill if you just want to walk.
Trains back to Chitose.
http://www.japan-guide.com/e/e6826.html

Day 3: Trail ride. The "Northern Horse Park" (Northern K? Park?) doesn't have trail rides. It's kind of a "watch the horsey" park with carriage rides, a small train, tennis, and other activities but not much on a horse.
http://www.northern-horsepark.co.jp/intro/ins-fee.php

There are some trail rides just south of Furano near the New Furano Prince Hotel that you might want to combine with the flower day at "Furano Yuma." You could also go up to Furano again or find a place to stay in the area so you didn't have to travel back to Chitose.
http://www2.ocn.ne.jp/~u-ma/index.html

Most Japanese are deathly afraid of horses and the tourist sites that I've seen with horse rides have somebody sit on top while another person leads the horse with the bridle around a path. I don't know how "Yuma" is but it's worth checking into.

The Trip-Advisor site gives the price for a trail ride ("Rindo Trekking 1-hour course")at Y10,000 for a 1-hour ride and Y18,000 for the "2-hour course." "Rindo" is "forest road." The review is pretty postive at:
http://goo.gl/uNr6GD
You can use the translate feature to get the gist.

There is also the "Haruka Horse Ranch" between Sapporo and Otaru that have 30 minute to 2-hour rides. They also have some expensive "Western Riding Style" lessons (I had to take English as a kid). This company also has branches at Lake Toya and Rusutsu.
http://www.jphorseriding.com/trail/
I like the disclaimer at the bottom that says that you might get the "smell of horse" on you.

I couldn't find anyplace that started with a "K" that was nearby, but that doesn't mean you haven't found it. As I said before, I've only been to Shizunai for horses but that was on business as Lexington, Kentucky is its sister city.

You can also use hyperdia.com to check rail schedules and fares.

Will do thank you so much! Will these still apply if I move my trip to end of September or will the flowers be out by then?

There should be at least the "kosumosu" blooming at that time (Cosmos). The site says there are other types but September is the end of the major blooming season.