Is it permissible for me to use money designated for a specific purpose, which has become inaccessible to me, to perform the Hajj pilgrimage for myself and my wife, knowing that I have no other money sufficient for Hajj before the next season? If that is permissible, is this permissibility restricted to Hajj only, or can it be used for any of my needs?

If you earmark money for charity with only the intention (niyyah (definition)), it remains your property, and you are not obligated to give it as charity merely by intention. You are permitted to dispose of it in ways other than charity, or to keep it, as long as you have not paid it out and it has not been taken possession of. If your intention was to allocate the money for spending in a specific area, there is no harm in spending it however you wish. The most deserving use for it, if you meet the conditions for its obligation, is to perform the Hajj pilgrimage.