Concealing my pregnancy..please read and help guys!!

I'm currently 8w1d pregnant and have got my booking in appointment on Tuesday 21st June. My appointment is at 9:30 and I have two issues: my oldest daughter starts school at 9am which doesn't give me too much time to get to the hospital unless I book a cab there. My other issue is my youngest daughter will still be with me as she doesn't go to nursery until the afternoon. My letter tells me to be prepared for the appointment to take up to two hours. I've got family members that could help me out with both kids that day, but as soon as I mention I have to go somewhere, I garuntee they will guess what's going on and I'm really not ready to tell them yet! My husband can't get the time off work to help me out. Does anyone have any ideas of what I could say I need to do for a few hours without the children? There's also no point in trying to change the appointment time as no matter what time of day, I'll need someone to help me with child care/ school runs! Any ideas will be gratefully received!