Many amateur radio repeater controllers have an "autopatch" feature built in, whereby one can "dial" the access code and phone number on their radio's DTMF pad to call someone. Some of them also handle "reverse patch" where the controller picks up an incoming call, the caller would then dial a code and the repeater would "announce" the call and someone listening can pick up the call. I've heard commercial controllers that do this as well - most commonly on a security frequency, if security gets a call but no one is in their office (after-hours) or at one college the emergency phones in the parking lot dialled straight to a patch setup on their frequency.
You would NOT be able to legally run encrypted on an amateur radio frequency. Further, what you can do over the phone is restricted on amateur radio. No business, no foul language, the usual restrictions. If you want more freedom on what you can do with the frequency, you'd have to get a commercial frequency license although they may also have some limitations - I don't know them.
If you are after a "cheap cell phone" alternative, realize that to most people on the phone side, a patch can be a right PITA. They are used to just talking, but now have to wait for you to unkey. It is VERY common to hear people repeating themselves often because they don't wait long enough to start talking.
Not sure what you mean by "trunking repeaters", you just need one repeater at the house with the phone patch. If you are so far away the handheld can't make it, you could use one in the car but it's often much easier to do a "cross-band" repeater in the car so you don't have to have all the isolation gear required of a traditional repeater. (Unless you intend to use 800MHz or such, where the components become smaller - but distance is greatly reduced without a very high antenna at home.) A cross-band repeater there would require the HT be dual-band, or always go through the car to get to the house.
This is really an awful lot of effort and gear just to talk on the phone - especially if you want privacy. A cell phone would be far more feasible!