According to the rules about building and modifying constructs, they are different process that work very much like each other.
The Craft Construct feat allows a spellcaster to create all manner of permanent constructs in a process much like magic item creation. [...]
Crafting a construct takes 1 day per 1,000 gp in the item’s base price, excluding any special material costs. This process is identical to the process for crafting a magic item, including the rules for accelerating creation and handling interruptions.
But nowhere it says they are the same process and can't be mixed together. The language used on these rules make it sound like it's a different process, or it wouldn't bother saying it's an identical process, it would say it follows the same rules, like every other feat of magic item creation that came after the core rulebook (example Inscribe Magical Tattoo).
That said, the restriction on downtime rules and magic item creation (one item per day) is so you limit the amount of wealth a character can generate in a single day. That limit exists even if you increase the DC to reduce the time taken, so the amount of time required to craft a single item does not affect the limit on one magic item per day.
If you GM house-ruled that you have two downtimes per day, then I don't see a problem with allowing to craft magic items (and constructs) twice a day as well. However, since he is house-ruling it, that is something only your GM can answer you.