There was no way that Spade had not considered this future when he let Liviera be part of this mission. However, after a lot of contemplation, he still decided to let his omega father be.
This was his grievance, and this was the only way for Liviera to ease all the anger that had accumulated inside his heart for years. This didn't mean that Spade wasn't scared that history would be repeated again and Liviera wouldn't walk to the same tragic end as in the last timeline; he was still so scared of this memory.
Spade only chose to trust his omega father this time. Liviera had undergone a change in his opinion of life, and he wasn't as destructive as before. Their conversation really helped a lot to ease both of their sufferings and misunderstandings.
It also helped build trust between them again.
"Let's go. There's no time to waste," Liviera calmly reminded them. His tone wasn't as imposing as his status.