Swing Pressure House

I have an impractical idea that may have beneficial effects for our space program: A house in which there is no carbon dioxide whatsoever, and it's all shunted aside to a greenhouse. This both benefits the plants, and is a security system for pests and vegetable thieves. We start with an oxygen generator, a machine who's name is a bit of a misnomer. It doesn't chemically generate oxygen so much as concentrate oxygen in the air. We want the industrial type, because it's cheaper, has higher airflow, and makes fewer assumptions about the air flow stream. This is used to pressurize an airtight house to 1.1 atmospheres. The higher pressure is to ensure that if any leaks do develop, the air flows out, not in.
Next, for dealing with the exhaled breath of the house's occupants, we have an airflow system that takes air from the house, and bubbles it through a hydroxide. All metal hydroxides react with carbon dioxide to form carbonates, which filters the carbon out of the air. Calcium hydroxide would be my primary choice, as this produces heat when synthesized, and is easily cleaned due to calcium carbonate being insoluble in water. You could even check visually to see when a hydroxide sample is worn down and needs replacement. Unfortunately, the synthesis of calcium hydroxide is more complex than sodium hydroxide, which can be produced by electrolyzing salt water. Enormous vats of hydroxides keep the air carbon free.
Over at the greenhouse, the metal carbonates produced by the air filtration system are bought to a lime kiln or vat of strong acid. The carbon becomes liberated from the metal, and spews forth throughout the greenhouse. This suits the plants fine, as the original earth's atmosphere was something like 30% carbon dioxide. As far as plants are concerned, modern earth is polluted all to hell with oxygen, which they produce as waste.
I wanted to make this a closed cyclical system, in which the greenhouse reset the conditions of the house, and vice versa. This would be necessary in space, where the gathering of additional materials is not possible. In space, if you did not bring with you, then you do not have it. I would recommend a calcium based system for this:
CaCO₃ + HCl → CaCl₂ + CO₂ + H₂O
H₂O + electricity → H₂ + O₂
CaCl₂ → Ca + Cl₂ H₂ + Cl₂ → HCl
Ca + O₂ → CaO
CaO + H₂ → Ca(OH)₂
Ca(OH)₂ + CO₂ → CaCO₃
On earth, a sodium based system is probably more practical: NaCl + H₂O → NaOH + Cl
NaOH + CO₂ → NaCO₃ + H₂O
CH3COOH + NaCO₃ → CH₃CO₂Na

You now have an endless supply of hand warmer and poison gas.