The following sections were the source of the post-conciliar development often troubling to lay people, bishops, and others: the placement of the tabernacle and the location for devotional prayer.
First rule, no problem: only one per church.
52. Where the eucharist is allowed to be reserved in keeping with the provisions of law, only one altar or location in the same church may be the permanent, that is, regular place of reservation. [See Codex Iuris Canonici (Rome, 1918) can. 1268, § 1.] As a general rule, therefore, there is to be but one tabernacle in each church and it is to be solid and absolutely secure. [See Sacred Congregation of Rites, Instr. Inter Oecumenici, 26 Sept. 1964, no. 95. Sources chretiennes Sacraments, Instr. Nullo umquam tempore, 28 May 1938, no. 4: Acta Apostolicae Sedis 30 (1938) 199-200.]
Then the preference for a separate chapel …
53. The place in a church or oratory where the eucharist is reserved in a tabernacle should be truly a place of honor. It should also be suited to private prayer so that the faithful may readily and to their advantage continue to honor the Lord in this sacrament by private worship. [See Presbyterorum ordinis no. 18. Paul VI, Encycl. Mysterium Fidei.] Therefore, it is recommended that as far as possible the tabernacle be placed in a chapel set apart from the main body of the church, especially in churches where there frequently are marriages and funerals and in places that, because of their artistic or historical treasures, are visited by many people.
… but a typically Roman concession to other possibilities:
54. “The eucharist is to be reserved in a solid and secure tabernacle, placed in the middle of the main altar or on a minor, but truly worthy altar, or else, depending on lawful custom and in particular cases approved by the local Ordinary, in another, special, and properly adorned part of the church.
“It is also lawful to celebrate Mass facing the people even on an altar where there is a small but becoming tabernacle.” [Sacred Congregation of Rites, Instr. Inter Oecumenici no. 95.]
If the Consilium waffles on the location of the tabernacle, we might conclude that theology has no bearing on the choice of its placement. That isn’t to say that the placement of the tabernacle isn’t a grave spiritual or devotional issue. It certainly is. But to claim as some do that the separate Eucharistic chapel is somehow a non-Catholic innovation is at best an inaccuracy, and at worst, a deception.