When I was in primary school we, as a class, were read at least two books involving a mouse with a toy motorcycle that actually worked, I really don't remember much else about the stories except that there was a sick child in the first one. I know that's not much to go on but any help at all would be appreciated.
The Mouse and the Motorcycle by Beverly Cleary
Ralph is a mouse who lives in the run-down Mountain View Inn, a battered resort hotel in the Sierra Nevada of California. Ralph longs for a life of danger and speed, wishing to get away from his relatives, who worry about the mice colony being discovered. One day a boy named Keith Gridley and his family visit the hotel on their way through California. Keith leaves a toy motorcycle on his bedside table, While Keith is away, Ralph attempts to ride it, but cannot figure out how to start it. Startled by a telephone ring, both Ralph and the motorcycle fall into a metal wastebasket.
Keith discovers his missing motorcycle in the wastebasket. Although Ralph's mother worries that he is in contact with humans, Keith shows Ralph how to start the motorcycle—make an engine-like noise—and lets Ralph ride it during the nighttime. While Keith and his family explore California, Ralph recklessly rides the motorcycle through the depths of the hotel. One night he is spotted by Keith's mother, and Mrs. Gridley thinks she is imagining things, but she is still sure that she saw a mouse riding a motorcycle. Ralph and the motorcycle are almost sucked up by a maid's vacuum cleaner, but Ralph escapes, riding into a pile of linen and dirty bedsheets. He escapes by chewing holes in the sheets.
After Ralph loses the motorcycle Keith loses trust in him, although he still brings the mice colony food. One night Keith becomes very sick because his parents don't have any more aspirin, nor are able to obtain one until morning. To regain Keith's trust, Ralph searches the hotel for an aspirin tablet, at risk to himself, for the medicine could prove fatal to a small mouse if ingested (in fact, Ralph's father was taken down with a bad cold and died in spite of all they could do). When Ralph is successful, Keith's health is restored. Ralph uses the space under the TV set in the lobby to use as a garage; the motorcycle is his to keep.
There are three books in the series: The Mouse and the Motorcycle, Runaway Ralph, and Ralph S. Mouse.