So forcible I don’t know about. Like strapping you down and giving you a vaccine against your will is probably illegal. But fines and restrictions that’s completely legal.
I agree, they cannot force you. For example if you do not want to vax your kids for MMR and polio etc..then they simply cannot go to public or private school, you will have to home school them but they cannot mandate you get a vaccine so you still have that freedom. SO the government does not force vaccination, it just makes it a requirement/mandatory. Private schools follow suit because they are certified by the state.
Same with COVID.. they cannot force the vaccine on you, just put in restrictions if you choose not to get it or provide a valid medical exception.