Just read OP and realised that there were a lot of questions I didn't answer.
There was no Conversation to be started. It just happened. DD went to university in South London, in the early 1990s when there was a huge property price slump but rents remained high and we worked out, that if she bought a 2 bedroomed property and rented a room out it was cheaper to buy than rent. She bought her flat for half the price it had been sold for 3 years previously.
We put little or no money into her house purchase but our most important contribution was DH acting as Guarantor for the mortgage. If she didn't pay he would. DH was checked out to see that he could afford the extra mortgage, as if he was applying for an extension to our own mortgage. As well as that we did all the property hunting, except viewing, helped her sort out all the formalities and acted as removals van, purchasing agent and decorators and plumbers. She (and her brother, later) each contributed £5,000 from money they had from regular savings we had made since they were born and a small legacy.
With DS 4 years later, it was different. House prices had risen a lot and he was in an expensive area. Here a fortuitous legacy helped. This provided 2/3rds of the price of a property and I took out a mortgage in my own name on the balance. DS supplied the deposit from his £5,000. Ownership was in our joint names. He actually paid the mortgage and all the costs of running the flat. An unexpected job change meant he needed to move out after 2 years. By that time the price had risen further and were still rising so as the mortgage was in my name, I took over paying it, paid him back his deposit and his share of the price rise and then renting it out commercially while he moved to a region where prices were lower and he was able to buy without any assistance from us as a first time buyer.
The key to the assistance we gave our children, which was financial facilitation, rather than actually giving them money, was that DD bought right at the bottom of a housing slump and DS bought when prices were rising, but had not reached their peak. Another year after DS bought and we could not have helped either of them as prices would have been too high.
No legal problems at all, we both fully understood what was required. DH just had to prove he could afford to act as Guarantor on DD's property. I bought DS's first flat jointly with him, with no exact share specified at my lawyers recommendation. This was so that if I died DS would own the whole property without it being included in my estate.
Emotions didn't enter into it. We did it to get our children on the housing ladder before prices rose too much for us to do this. We wouldn't change anything we did. We got both children on the housing ladder, at minimal cost to us and them when prices were low, but circumstances in the housing market have changes so much that what we did is not repeatable.