If everything is so amicable then why not remain in the family home until it is sold? If you are putting your child first they would benefit from this continuity.If things are so amicable why does your wife want you out of the family home so quickly? You need to protect yourself and listen to the advice from the experienced on here.
I fear you are being very naive and trusting,but as has already been suggested you need to seek legal advice as your wife has done.I also am concerned that whatever advice you are given by what you might see as the cynical amongst us you will ignore.You only have to read many of the horror stories on here to discover what started out with promises of being an amicable divorce, ended up in long drawn out horror stories.
I agree Crimsonlake as I was naive at the beginning. Soon learnt you have to be on your guard at all times. Saying that I suppose some people are fortunate to have an amicable divorce. I just found that as soon as the solicitors got involved it became more of a battle but I know solicitors are doing what their client tells them but at the time I believed my ex could do no wrong realise I was a fool to believe that.