For all intents and purposes you will need to forget that the child is 3 and treat him the same as you would a new one year old - the scenerio is the same in the sense of first separation but compounded by the two extra years of personal treatment.

Ignoring rather than trying to engage will likely be your best bet. Go about your normal things with the kids and if anything plan extra whole group activities. Hopefully he will show interest in what you have gotten out to show the children or the story you are reading, etc. but let him do it at a distance. Over the next few days he will likely start to come closer and closer when you do the activity or at least you will be aware that he has started paying attention. Then switch to things with pieces where you give each child something to take part. Encourage him to take his turn but give him a figure you can sort of ignore if he doesn't such as doing old macdonald's farm - who cares if the goat doesn't come to the farm.

Diapers - you maybe able to reason with him over the next few days using that firm voice that indicates sorry you don't have choice in this. Sometimes up on something for changing such as a bed or the coffee table, on the floor use a mat - something that defines the space he needs to stay in such as the nap mats or I use two of the 2x2 foam squares for my special needs daughter who no longer fits on anything obviously. You might also have success changing him in a confined space such as between the couch and the coffee table - where he has limited space to move around in. You could also insist on pullups and then change him in the bathroom having him sit on the toilet with an insert so he doesn't have to support himself - pull off one and put on the other. Doesn't get to wash him but at least he gets changed. For poops it is the floor and no choice.

Anytime you try to interact with him it just reinforces the fact that you are not mom AND you are not nanny - he is feeling the loss of two people and especially if the nanny left suddenly. Likely he will first open up to the other kids and then gradually join into things they are doing with you.

Don't discount using the tv as a transition during this time for him since it might be one of the only familiar things for him from home to daycare. Move from there to stories based on tv characters or a game with charater shapes such as holding a shape or colour. Talk more and more to him but don't expect him to talk back.

How long it takes him to settle in will depend on how stubborn he is, lol. But as mentioned above, once he has adjusted he may turn into one of your best kids.