im having a lot of trouble getting the sufficient gold/provisions/supplies to give emily when she leaves with her sister, fandom wiki is no help as usual.
You don't need to give them gold and food to get them as slaves, but you do if you want to progress along that quest line. The amounts are 50 gold and 50 food, which should be trivial amounts, especially since you have at least 7 days before Tisha appears after you invite Emily into your mansion.
For an easy start, I play as a Halfkin Wolf Hunter, put 2 points into agility, buy and equip Chain Armor, and then explore the Outskirts of Wimborn for bystanders to rescue from thugs. I use the rewards I get from the bystanders to buy bandages and fight until I have enough gold to buy full gear for my combat group and 1000 to 2000 spare gold. While Emily cannot be used as part of the combat group immediately after inviting her into your mansion, an experienced player can use a Meet interaction to boost her obedience and loyalty to the levels required for the combat party (the Bugfix mod can help clarify why people cannot join the combat party). Then I buy 3 supplies and use the "Rest and eat" option to remove all stress from the combat group before I assign jobs and end the first day.