I think aiming for December 2021 seems like a good idea, summer is possible but a bit more questionable.
In theory Newsom is not requiring to open DL, and he hasn't mentioned including it in his tier system (though it could change). It's the number of coronavirus cases and hospitial utilization that are most important. I expect he will continue to have some form of the same tier system we currently have. Of course, the vaccine is one of the main keys to keeping the virus in check. However, there might be a few reasons things could be more optimistic than we might expect. First, the number of cases doesn't have to be zero, just has to be "low enough" for DL to open. We don't know how many vaccines it will require to achieve that, but I don't think it will be like 100% of the population. Even just some people getting the vaccine will help the numbers somewhat. Additionally, there is some % of the population that has some immunity since they have already had Covid, so we're not starting from 0% technically. They say that the US should have 40 million doses (for 20 million people) by the end of the year, so that may help at least make a dent. Also, the Pfizer vaccine does have some efficacy even after the first shot, though it's only around 50% after 1 shot vs 95% with 2 shots, but again it's better than nothing, and maybe help the Covid numbers a bit faster. Finally, since high risk patients will be getting the vaccine earlier, you might expect hospitalizations and mortality to decrease disproportionally to the Covid infection rate (hopefully), which maybe will help things open up faster as well.
Take this with a grain of salt since this is all just personal speculation (it is the DL Reopening Speculation Thread after all, lol).
Regarding kids getting vaccines, that will not happen for a long time since it has not been tested in children, though Pfizer and Moderna report they are starting those trials now (though Pfizer is only 12 and up, so not sure what will happen with young children). I suspect it will not be approved for children tomorrow.