Window Unit or Portable A/C - Includes a high quality, expert-drawn MS Paint composition!

tl'dr - Install window unit in kitchen window or purchase portable unit that could be moved around the house? Or other idea that doesn't involve reworking ductwork?

My landlord built some additions to this house about 8 years ago and didn't account for the amount of air flow he would need. Further, according to an HVAC specialist that looked at the system a few weeks ago, the ductwork isn't built correctly and pushes a ton of air into the master bedroom and adjacent guest bedroom. The blower is just underneath the master bedroom. The air flow is a trickle as you move to the other end of the house, and the kitchen is almost always warm once the sun comes up.

With the current heat wave we're having, it's getting miserable in our house by the time 4pm hits. I understand that 95+ degree weather will be hard to keep cool in an older home that has insulation problems, but I'd like to try to regulate the temperature better.

Here's what we're doing so far:

We have a dehumidifier that runs in the playroom. We keep the unit fan blowing constantly and all ceiling fans on (every room has one). We try to keep the a/c running, but I fear it freezing up on me from too much use. I will occasionally throughout the day turn it off for a few minutes and then set it back on.

Even with that, my daughter's (10 months old) room will read 77-78 degrees from 8pm until around midnight and might get to 73 by early morning. We keep her door open to the hallway that goes to my son's bedroom. We keep his door open with a small fan blowing from his doorway towards her room. I think it helps, but it's still too warm. We keep the door from her room to the kitchen closed to block out the warm air from the kitchen to her room. We keep the vents closed to our room and my son's room, but the registers can't really block it too much because of the wind speed.

I think it's because the kitchen is so warm with so little airflow that my daughter's room (which has no windows and a trickle of air from the registers) can't cool down. If I install a window unit into the window of the kitchen to keep the kitchen cool, will that help bring my daughter's room temperature down?

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