“My husband and I have sold our house and are thinking of moving into a new place with our daughter and son-in-law. We intend to put some of our capital into the new place – is there any reason why we should have a formal arrangement in this respect?”
The answer is most definitely yes. You should enter into a Deed of Trust with your daughter and son-in-law which means that should the house be sold then you would receive back the capital that you put into the property. Your interest could be expressed as a percentage of the value (or the equity) at the time that you invest the money and then you would receive that percentage of the property in the future and hopefully the property will increase in value.
There are several reasons why this is sensible. For example if things did not work out with the living arrangements and either you fell out with your relatives or it was just difficult to live together. You would need to be able to extricate yourselves with capital to rehouse yourselves.
If your daughter and son-in-law divorced then you may not want the money to go to your son-in-law or even to be divided between them and all the time you have no registered interest then this could happen.
It's better to be safe than sorry!