I don’t believe I am. It doesn’t say τῷ υἱῷ ἔδωκεν ζωὴν “he gave the son life.” It attaches an infinitive to it, which changes the meaning of διδόναι. It reads τῷ υἱῷ ἔδωκεν ζωὴν ἔχειν ἐν ἑαυτῷ “he allowed/permitted/authorized the son to have life in himself.”
The part where it goes on and has an infinitive after it. You’re not translating the whole phrase. It’s not so much unclear as it is poorly translated.
The infinitive only strengthens the original assertion. There is no difference between saying “God gave the son eternal life” and “God gave the son to have eternal life.” You have to show proof that ἔδωκεν with infinitive becomes an idiom which transforms the meaning of ἔδωκεν to something closer to “allowed.” I haven’t seen any evidence so from the Greek for your assertion.