Can you stow the trailer at the daycare? People do that with car seats sometimes. At one daycare I saw that going on so I asked about my kid seat and they said no problem. At another, they were flummoxed but said yes.
This was a few times a week with kid 1, and hard work. Now with my twins I’d find a different solution that would likely involve an electric long tail, but they haven’t gone to day care.