“Is he also claiming that Transubstantiation does NOT occur in an Episcopalian church service?”
Undoubtedly. I’d maintain the same thing. Aside from some baptisms, the only sacraments which Orthodoxy and Rome accept are those of each other.
“If my children were with me at a Catholic Mass I would not hesitate to take them to Communion since they have already received at the Episcopal church we go to.”
The Episcopal ecclesial group is not in communion with the Pope of Rome, nor with any of the Orthodox Churches. What is the basis for your presumption that it is proper to approach the chalice in a Latin Church? The discipline of the Latin Church forbids it. It allows me as an Orthodox Christian to approach but my Church forbids me to do so. My Church also forbids you and anyone else who is not Orthodox, including Latin Rite Catholics, from approaching. Sadly, what you propose, namely that you will decide what the discipline of The Church should be regarding communion, has lead to the necessity in many Orthodox Churches for the priest to announce before communion that it is reserved for Orthodox Christians in good standing who have prepared themselves by fasting and confession according to the disciplinary canons of The Church.
The way I understand it, the only time an Orthodox believer is allowed to approach a Latin priest (allowed by Rome, that is) is in case of grave emergency. And Latins are allowed to approach an Orthodox priest in similar circumstances.
But in grave emergencies only, not as a regular practice.