Same as I think joining was the most ill thought-out, self-harming, illegal and disastrous act that any UK government has implemented in the last 52 years, after the most blatant lies were distributed by its supposed leader of the day.
The UK's "power and rights" in the EU were steadily waning after Thatcher, with opt-outs and rebates already largely bartered away by Major, Blair and Cameron. In 2015, the EU was pushing for its own army, finance ministry and foreign ministry, and well on its way to achieving the dream of creating a single European super state, whereby the UK would have eventually become a mere vassal province. Should the UK rejoin, then all these ambitions and dangers would resurface.
I agree that by rejoining the UK would be in an even weaker position than before. But but I also think that If your children are determined enough, then they will still be able to move and work in the EU or elsewhere.