What it means
うにも〜ない expresses that even if someone tries or intends to do something, circumstances make it impossible. The first verb is in the volitional form, followed by にも, and the second predicate is normally the same or a closely related verb in the negative form. It often conveys frustration, helplessness, or an obstacle that prevents the intended action.
Usage note
The first verb is not an ordinary conditional; it presents a deliberate attempt or intention. The negative predicate is frequently a potential form, as in 建設できない, but other negative predicates are possible when they clearly describe why the intended action cannot be carried out.
How to use it
資金が不足していて、私たちは新しい研究施設を建設しようにも建設できません。
Because funds are insufficient, we cannot build a new research facility even if we try.
資金が不足していて、私たちは新しい研究施設を建設しようにも建設できない。
Because funds are insufficient, we cannot build a new research facility even if we try.