Is it possible to collect all the girls before our day is over?
Yeah, though Maelys is a bit of a odd duck.
You have to go to the forest on Act 2, either force her to get dicked by the horses or let her go for Despair and Doubt paths respectivelly.
The Cat-Girls need gold to get them, build traps.
You get Cooch/Merc Girl anyway if you recruit the mercs, but it's also a good idea to get her before so you may do the Heist with Mina to get more Gold.
Mina either starts pissed off or neutral, but she will always become pissed if you ally with the Mercs.
So forth, you can get all the girls in act 3 with many days to cover that.