Hi neb,
Sorry to hear about your sad loss, but what a lovely idea you have in memory of your cousin.
The following advice assumes you are from the UK. If not, you will find similar software for your country from a quick search on Google.
There are many photobook business's that will fulfill your criteria. Here are some of the more recognised ones that will allow you to download free software, or use it on line, or both, so you can compose exactly what you want. The beauty is you can start a project and leave it open so you can come back to it as often as you like before committing it to publication. My advice is for you to go to the suppliers websites and see which software best matches your needs.
Blurb
Jessops Photo (cewe software)
Aldi print software
Myphotobook.co.uk
The above all have links on their websites to the software you can download free of charge. This is not a comprehensive list, just a few suppliers that I have downloaded in order to view their software. Blurb is probably the most established from this list but there are many others to choose from. Other members here will have their favourites and I'm sure they will add to this list.
I don't know for sure, but it may be possible to set up a password enabled account with one of the on line software suppliers that would allow friends and family members to access a Photobook started by yourself, so they could then add their contribution in exactly the way you describe. If that isn't possible, then an alternative may be to choose the best downloadable software that suits your needs, get all those involved to do the same, and send one of them a saved file of any work completed so far for them to add to. Once saved it could be sent back to you to send on to the next contributor and repeated for all contributors.
Hope this is of some use, and welcome to the forum.
All the best,
Rick.