You say that you have encouraged your son to buy a flat, has he already done that?. If he has your second option is unlikely to be feasible, as the odds on him qualifying for a second mortgage on the income of an 18 year old are unlikely.
If buying with you is an alternative option, yes that would be feasible as long as he qualifies for a mortgage of the amount required.
Here I will give my usual caveat that I have been retired a few years now so am getting out of date with any new rules in the industry.
You would have to think carefully about how you would all own the property to protect your daughter's inheritance and insure fairness between them. It would be advisable to register as tenants in common with each person's percentage share in exact relation to the amount they are putting in. This would be done by the Solicitor on purchase. Whilst your daughter is still living in the premises she would have to sign a Letter of Consent' which just confirms that she knows the property has a Charge on it and if repossession is ever required she would have no right to stay there.
Each Bank/Mortgage Company has it's own guidelines, so it would be a good idea if you made an appointment for the 3 of you and don't be surprised if they insist on your names on the Mortgage, this would give them protection if your son ever defaulted as they could come to you to demand payment.
As far as inheritance is concerned you and your wife could do mirror Wills, leaving your share to each other, and on second death divided between both children. This would mean your son retains his share and half of yours and and your daughter the other half.
There would be things to talk about within the family, on second death if your daughter needed her share within a short time would your son have the funds to buy her out? What happens if he meets someone in the future and wants to buy a property with them, is he going to want you to buy his share and will you be able to? plus many more questions I am sure you or your children will come up with during discussions
Before going any further it would probably be a good idea for your son to go on a couple of Mortgage sites to ascertain if he could actually get a mortgage of £100,000.