My advice is not specific to Matrix but other self hosted private services. Some of this may or may not be feasible with Matrix. (I have never used Matrix)

- Whether family or friends, always suggest it as a "fallback" for when "preferred service" is down and to use when discussion ultra-sensitive topics or sharing financial files. With time they may just stay connected to it if the friction to do so is low. It has to be their choice, not yours.

- What helps? Add more incentives such as perks that "preferred service" does not offer. No file size limits. No or few file type limits. No content filters. Add emoji's or gifs that align with their inside jokes and their style of humor. Keeping random people away is very important. Making your friends and family administrators or moderators and let them decide how it operates. Do not moderate or power-trip over your friends or family or they will leave. Limit rules to "Do not break the laws of this country in public chatrooms" and private chat rooms if you do not physically host the server. Database and file backups become even more important but they will feel in control of a thing. Have a keyword or code word they all learn means to go check the private platform that "primary platform" would not recognize. Maybe when they see "Turtle Farts!" they know to go log into your service.

- They may just stay on their primary preferred service. Every group is different and not every group will see the benefits of your fallback service. They may not appreciate the work you put into setting it up for them. Do not expect to get the friends of your friends and family to move to your service. They may not appreciate the OpSec value until "Bad Things"(c)™2038 happen to enough people. Just be there for when it does.

- If there are concerns that you would spy on them, consider instead using eJapperd or Prosody as you can implement OMEMO for individual and group end-to-end encrypted messages. Set up TLS fingerprint checks from multiple locations to reduce the risk of MitM attacks until XEP-0474: SASL SCRAM Downgrade Protection is fully supported and active by default on both servers and all clients. This is the only thing holding me back from setting up a public Prosody server as 0474 is still experimental. See [1]

- Avoid (block) federation on private servers for friends and family otherwise it is not a private server.

[1] - https://news.ycombinator.com/item?id=37955264