If you're doing the away in August, you are not going to be able to ask them for a letter until end of August which pushes you getting the letter into middle of September - yes, that is too late. You will miss some deadlines, other deadlines you won't miss per se but your application would be in on the late side, some schools will already start sifting through their piles and selecting interviews and you don't want to be left out of that pile (even if interview invites are not officially out yet). Timing is the last thing you want effecting your match, I just wouldn't risk it. Your goal is to have your letters in your possession by end of July and submit as early into August as possible, inevitably letter writers always run late and delays happen even given this timeline. Nothing wrong with 2 letters from your home program, just make sure they are as strong and personal as possible.