Hi there Alina,
Thank you for making a magical stop here at the Disney Parks Moms Panel. I'm so sorry to hear about your child's illness… sending them happy thoughts and pixie dust.
The Disneyland Resort does not offer partial day tickets unfortunately. You will have to pay the full ticket price. However, there are areas for breaks throughout the parks and magical options beside attractions that your child can still experience. They can enjoy shows, parades, Meet 'N' Greets, character dining, live performers, the fireworks, and so much more.
With your child's recent diagnosis, you may want to visit Guest Services located at City Hall once inside Disneyland park to see if the Disability Access Service (DAS) Card would benefit your child while at the Disneyland Resort.
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Disability Access Service (DAS) Card is designed to accommodate Guests who aren't able to wait in a conventional queue environment due to disability (including non-apparent disabilities). You will visit the main entrance Guest Relations to discuss your child's special needs and concerns with the Cast Member to see if the Disability Access Service Card (DAS) would benefit your child's needs. This is determined case by case. The child's photo will be taken for the issued card. The Cast Member will review all the guidelines of the DAS card with you.
I hope this helps and that you have a pixie-dusted visit. If you have any more questions, please visit me here and let me know how I can help you plan your magical vacation.
Wishing you magic!
~Lynette