1to go into; to get into or penetrate (to enter into a space or area)
猫が段ボール箱の隙間に入り込んで動けなくなった。
The cat got into a gap in the cardboard box and couldn't move.
彼は人混みに入り込むのが苦手だ。
He's bad at mixing into crowds / doesn't like getting into crowded places.
雨水が靴の中に入り込んでしまった。
Rainwater got into my shoes.
2to become complicated; to have extra elements enter (making a situation or story more complex)
交渉に個人的な感情が入り込んで話がややこしくなった。
Personal feelings entered the negotiations and made the discussion complicated.
問題に余計な条件が入り込んで解決が遅れている。
Unnecessary conditions got involved in the problem, delaying its solution.