How can I connect a faucet adapter to a non-standard faucet without leaks?
Take the aerator from your faucet and the adapter from your dishwasher to a plumbing supply store. They will have a bigger selection of sizes. It is possible you have an unusual faucet that HomeDepot doesn't carry. Do not use superglue. If you do anything to alter the fixture you could be responsible for replaceing it when you leave.