Hi Chloecat, welcome to TP
I think you may struggle to find day care that will take someone who in his situation.
Most of these places aren't "secure", the staff ratios are often quite low and they have no right to keep him there against his will, if he wants to leave they have to let him, they're not allowed to physically stop him and if they tried there is always the possibility he could become aggressive with strangers.
Legally to detain an adult care home use a Deprivation of Liberty Safeguarding order (DoLS), sometime people are detained usually under section 2 or 3 of the Mental Health Act and of course the police can arrest you and a court send you to prison, outside these and similar legislation no one has the right to detain someone against their will, that's what the day care people are up against, if they detain him in any way they're breaking the law.
Respite care is different as they could get a DoLS and somewhere that is secure could keep him there, several people in care with my wife would be out the door given half a chance so all the doors are key coded, you need two different number to get in or out (so 4 in total) and we're all aware you don't open a door if a resident is too close.
Sorry that's not good news all I can suggest is you offer to stay, see if he fits in and they agree to taking him without you after a time.
K