Dear Paula -- thank you for posting to History Hub!
I'd recommend starting with A Century of Lawmaking, a website from the Library of Congress that's digitized many of the records and acts of Congress from the Continental Congress through the 43rd Congress.
From the search page, look for "John McDaniel" and limit the results to the 36th Congress using the drop down menu. The first search result is a link to H.R. 642, 36th Congress -- "For the relief of the surviving children of John McDaniel, a soldier of the revolution." It does not look like this bill was ever passed into a law.
The other three results are from the House Journal -- on Feb. 17, 1860 a petition was submitted and referred to the House Committee on Revolutionary Pensions; on April 13, 1860 H.R. 642 was reported out of committee to the Whole House accompanied by a report; and on March 2, 1861 the papers of the children of John McDaniel, among others, were withdrawn from the files of the House for reference to the Commissioner of Pensions.
Given that the papers were referred to the Commissioner of Pensions, I would not expect to find record of the McDaniel family among the records of Congress. According to the Federal Records Guide, the records of the Commissioner of Pensions are part of RG 15 -- Records of the Veterans Administration.
If you'd like to find the report accompanying H.R. 642 mentioned in the Journal (it's numbered H.Rpt. 36-424), I recommend finding access to ProQuest Congressional, a subscription database with the full text of the U.S. Serial Set -- which has the published reports and documents of congressional committees. ProQuest is usually available through local academic and law libraries. It's also available through computers at National Archives research locations.
The Center for Legislative Archive, a unit within the National Archives, holds the official records of congressional committees and the records of the U.S. Senate and the U.S. House of Representatives as a whole. I did a quick check in the petitions referred to the House Committee on Revolutionary Pensions in the 36th Congress, as they're arranged alphabetically by claimant, but unsurprisingly (per reference above) I did not see anything.
If you have further questions, you are welcome to email the Center for Legislative Archives directly at email@example.com.
Sarah, thank you for all the information! Paula