I don't think its the Day Centre's fault. They are probably restricted in what they are allowed to do. I was told by ours that they can give pills but they can't keep meds on the premises, so the antibiotics had to travel back and forth each day. I assume if you work somewhere you have to be trained to be allowed to give injections.
Hopefully a GP can arrange someone from community services to help.
I'm speculating here, but I wonder if it's not so much the giving the injection (I have a friend who's a type 1 diabetic and when she injects herself it's in the leg, through her clothes) but more the testing before hand, the requirement to read the test to ensure you aren't giving too much or too little insulin, the need to make sure you don't inject in the same site every time: basically the whole thing. And I have to say, I wouldn't want an untrained person to be injecting me with something that could actually kill me if they got it wrong, nor would I be willing to put any of my employees in that position.
I think Tina's idea about a district nurse is probably the only option. That or perhaps instead of one "day" at day care, two half days so insulin is still given by you.