Two Hands, surprised to read your bedroom is getting so chilly while downstairs stays warm. We have two A/Cs and if we didn't use the bedroom A/C during the hot CA temps, our bedroom will get quite toasty because warm air rises. We arrived in Hemet on 9/21 just in time for some of the 100s days. Both A/Cs were cranking and it was still difficult to cool downstairs. During the day, we sat a fan in the floor of the bedroom facing downstairs in order to send additional cold air downstairs.
Our position in the park has the sun setting on our window side which doesn't help the cooling process. We have not yet purchased the silver insulation that so many folks here use. Now that temps have cooled down, we are enjoying open windows. Our Lady Kitty appreciates that very much also.
We recommend you get the second A/C anyway but also suggest you have your airflow investigated. There may need to be some taping done on any open areas inside the filter cover. Ours had several open areas that required taping and that definitely improved the cooling ability for downstairs. As porthole recommended, sometime we also use the 'quick cool' method on the filter cover so there is a direct down flow of cold air into the kitchen/living room area (useful when cooking).
Note: Several of us use the bedroom A/C as a 'sound filter' so we sleep better at night. Lessens the outside sounds of trains, traffic, barking dogs, etc. CJ