Putting the d~ and ees~ inside the <<...>> block gets a bit closer. You can see the ties, but has other differences from your original example. I'm not sure exactly what your final goal is:
\relative c' {
<< { d16~ \once \override NoteColumn.force-hshift = #-0.6 \once \override Stem.direction = #DOWN d2 }
\\ { ees16~ \once \override NoteColumn.force-hshift = #0.6 \once \override Stem.direction = #up ees2^\trill } >>
}
OR
\relative c' {
<<
{ ees16~ \once \override NoteColumn.force-hshift = #0.6 \once \override Stem.direction = #up ees2^\trill } \\
{ d16~ \once \override NoteColumn.force-hshift = #-0.6 \once \override Stem.direction = #DOWN d2 }
>>
}