I'm pretty sure that here 手に入れる is てに入{い}れる. I don't know if it is ever used as てに入{はい}れる because this seems like it would be confusing, but if it is, this is rare. (That being said I think you do hear 入{はい}（ら）れない as "it won't fit", but someone should check me on this). 手に入れる means to obtain, just like 入{はい}る, so I needed to search to find an answer to your question. Apparently, the nuance with 手に入れる is that it is difficult and/or more effort was made to obtain, and that 手に入る is with not so much effort, such as finding something and picking it up, or being given something, etc.
That being said 手に入れる can be a result of luck, such as winning the lottery, but this is considered something that is difficult to obtain.
The example that helps me remember is in RPG games when it uses 経験値を手に入れた after defeating monsters (requiring effort), to mean "obtained experience points". You will probably never see 手に入った in this case.
For this problem, we should assume that the speaker is just saying "it's hard to get tickets for this team" in the general case - that is, without spending some great deal of effort.
On top of this, なかなか手に入らない is a common saying in my experience and backed by google - it gets 24 million hits vs なかなか手に入れない and also has a definition in alc as 'hard to find/be rare to get/be always unavailable' vs the other's 300k hits on google (using quotes of course) with no entries in alc.
Lastly, for completeness, here's an excerpt I found on the web that explains the two use cases in japanese.
From http://lang-8.com/231058/journals/800177/%25E3%2583%25AD%25E3%2583%2583%25E3%2583%2588
あ、ききわすれた、"手に入れる"と"手に入る"は違いますか？
Feb 09th 2011 17:46 aico
すごいギャンブラー精神だ！
中国の人もギャンブル好きだよね。世界中のカジノって中国人客がすごく多いみたい。
あ、ききわすれた、"手に入れる"と"手に入る"は違いますか？
何かを「獲得」という意味では同じだけど、
手に入れる<<何か努力や行動を起こして獲得。
・ロトで10億円手に入れる為にすべての財産をなげうってロトを買った。
手に入る<<誰かにもらったなど特に行動を起こさず勝手に獲得。
・美味しい皮蛋が手に入ったよ〜。台湾人の友達がお土産でくれたんだ。
