Hello! I'm glad to hear that your parents arrived safely.
I checked a homepage of Iiyama Onsen, the hotel's name is Motoyu ryokan (元湯旅館), in internet.
There are courses at day time that you can chose as follows.
1. Yuagaribijin Delax course 9,500 yen
a seasonal lunch and public baths with Yukata, bath towel and towel
2.Yuagaribijin course 7,300yen
a seasonal lunch and public baths with Yukata, bath towel and towel
3.Yuttarikaiseki course
A course : 11,550yen
B course : 9,240yen
C course: 6,930yen
a seasonal lunch and public baths with towel (no Yukata)
I think the difference of the corse is lunch.
The lunch become better as the price more expencive.
You can use a guest room and eat lunch with your parents at the guest room whichever you choose any course.
The guest room is private room so you can eat just you and your parents.
All courses are you can use a guest room and baths at 11am ~ 14pm or 15pm.
But, When I went to there with ayumi before, I arrived at 16pm. So, if you want to arrived at 1:00pm, I will call the Motoyu ryokan to ask a hotel man that you can use a guest room an baths at 1pm to 4pm or 5pm.
When I went to Motoyu ryokan with ayomi before, I took C course of Yuttarikaiseki course.
It was so nice!
The spring quality of onsen is strong alkali. That is very good to skin.
The water makes your skin smooth!
Please tell me which course you like, and I will make a reservation!
http://www.motoyu.co.jp/index.html is a homepage of Motoyu ryokan.