tnason:
The others who have responded to your initial inquiry have fleshed out the issues quite well.
While is it good to have verbal confirmation from the photographer that you will have the ability to print picture for personal use, the language of the contract does not appear to support that interpretation. Indeed, ". . . Clients agree not to publish the photographs without permission of the photographer. Clients will have unlimited personal use of the photographs at any time for no additional fee. . ." explicitly states that you, as a client, cannot publish the photographs without permission of the photographer. It is also unclear from the language provided whether "personal use" would include "publication for personal use." Likely, there is another part of the contract specifying that the permission must be in writing, and that the contract reflects the entire agreement between the parties.
Since this is important to you, you might want to add language to the contract clarifying the meaning of "personal use" or otherwise specifying that the Client shall have the right to reproduce photographs for personal use without the photographer's express permission.
An alternative, but less desirable way of handling the situation would be to summarize your recent discussion with the photographer in a letter. The letter should state something to the effect of, "pursuant to our discussion on DD/MM/YYYY, we mutually understand and agree that "personal use" as defined in the contract for photography services means, without limitation, that I have the right to reproduce photographs produced in accordance with the contract without your permission, provided that such reproduction is for personal use only (e.g., for distribution to parents, inclusion in personal albums, etc.). Notwithstanding the foregoing, this letter is a record of the oral permission conveyed by you on DD/MM/YYYY, indicating that I may reproduce photographs produced in accordance with the contract, provided that such reproduction is for personal use only."
Best,
Klav