No... I'm not exactly sure what you're trying to say, but it sounds like Theopaschism (the heretical belief that all three members of the Trinity suffered and died on the Cross) mixed with Sabellianism.
Only Jesus suffered and died on the Cross, because only Jesus became man--the Father and the Holy Spirit did not become incarnate, and so did not suffer on the Cross.
Interesting. Admittedly, based solely on chapter 11, I can't make heads or tails of what Ignatius is saying here; this is one case where the longer recension actually makes a lot more sense.
Shorter recension:
Flee, therefore, those evil offshoots [of Satan], which produce death-bearing fruit, whereof if any one tastes, he instantly dies. For these men are not the planting of the Father. For if they were, they would appear as branches of the cross, and their fruit would be incorruptible. By it He calls you through His passion, as being His members. The head, therefore, cannot be born by itself, without its members; God, who is [the Saviour] Himself, having promised their union.
Longer recension:
Do ye also avoid those wicked offshoots of his, Simon his firstborn son, and Menander, and Basilides, and all his wicked mob of followers, the worshippers of a man, whom also the prophet Jeremiah pronounces accursed. Flee also the impure Nicolaitanes, falsely so called, who are lovers of pleasure, and given to calumnious speeches. Avoid also the children of the evil one, Theodotus and Cleobulus, who produce death-bearing fruit, whereof if any one tastes, he instantly dies, and that not a mere temporary death, but one that shall endure for ever. These men are not the planting of the Father, but are an accursed brood. And says the Lord, Let every plant which my heavenly Father has not planted be rooted up. For if they had been branches of the Father, they would not have been enemies of the cross of Christ, but rather of those who killed the Lord of glory. But now, by denying the cross, and being ashamed of the passion, they cover the transgression of the Jews, those fighters against God, those murderers of the Lord; for it were too little to style them merely murderers of the prophets. But Christ invites you to [share in] His immortality, by His passion and resurrection, inasmuch as ye are His members.
At first blush, it would seem that you're right. But, let's put chapter 11 in context:
9.
Stop your ears, therefore, when any one speaks to you at variance with Jesus Christ, who was descended from David, and was also of Mary; who was truly born, and did eat and drink. He was truly persecuted under Pontius Pilate; He was truly crucified, and [truly] died, in the sight of beings in heaven, and on earth, and under the earth. He was also truly raised from the dead, His Father quickening Him, even as after the same manner His Father will so raise up us who believe in Him by Christ Jesus, apart from whom we do not possess the true life.
10. But if, as some that are without God, that is, the unbelieving, say, that He only seemed to suffer (they themselves only seeming to exist), then why am I in bonds? Why do I long to be exposed to the wild beasts? Do I therefore die in vain? Am I not then guilty of falsehood against [the cross of] the Lord?
11. Flee, therefore, those evil offshoots [of Satan], which produce death-bearing fruit, whereof if any one tastes, he instantly dies. For these men are not the planting of the Father. For if they were, they would appear as branches of the cross, and their fruit would be incorruptible. By it He calls you through His passion, as being His members. The head, therefore, cannot be born by itself, without its members; God, who is [the Saviour] Himself, having promised their union.
Also, keeping in mind that it's always, always always Christ Who is the head of the Church, and not the Father (see Ephesians 4:15, 5:23), and that it is always the Father Who plants (see Matthew 15:3), it becomes clear that the "Father" only refers to the planting. Even though Jesus' name isn't used in the sentence in question, the sentence is clearly referring to Christ--hence the elaboration made in the longer recension.
So, even though we today have Ignatius' epistles all in chapters, originally they were just letters, and the chapters didn't exist, but were later additions meant to chunk it up and make it easier to read.
Yes, Trinitarians have no problem with this.
Take out the Father being on the Cross, and clean up the Christology you mentioned to reflect the Hypostatic Union, and explicitly acknowledge that the Father, Son and Holy Spirit are all three distinct Persons, and yes, that's Trinitarian.
[quot]Look up Sabellism for more on Oneness believers from ancient times. They did exist, we just don't know as much about them because the trinity doctrine became more widely believed as time went on. After all it was eventually adopted officially by the Roman Empire; from which we have the two so called Catholic churches.