TBH it's times like this I enjoy, as it makes me inspect and investigate things you wouldn't normally do, which builds on the knowledge you gain, so it's all good, but I do fear additional hardware would be needed at this time, your speaker issue tells me either speakers are treated like headsets, only 1 at a time, or it does not have multi connectivity, as best as I understand such matters currently anyway.
Bluetooth will work in theory, but as it is so heavily influenced by it's surroundings it may not be a way the big names will be looking at, Wi-Fi seems to be the way the big names are going, probably because it has a stronger ability and range, and the tablet range is probably 10M at the most, but you can get Bluetooth dongles that can reach up to 250M, so if you were to pursue this idea a dongle on your PC is the most likely start to get you a result.
Also the multi connectivity of such a dongle has a much better chance of working, but the more I see the more it seems most treat the speakers like a headset, so although you can have the headset, PC, car connected at the same time, and still be able to send a file to another phone, I fear as far as audio is concerned it's a way off yet before doing what you want.
But that said, there are options around that get close to what you want, JAMBOX connects to more than 1 speaker, and their Boombotix Sync App is showing a lot of promise in what you want to do, and there are various Bluetooth hardware options around where you "may" get to achieve your goal, but I would not go down that road at this time.
Big Update, the answer is a definite NO, not at this time at least, MultiCast is the main term here, and although you can connect to multiple devices at once, it appears to be you can only connect to 1 of each type at the same time, and even if possible you could not transmit different media (songs) to different speakers at the same time, so even if you can get more than 1 speaker connected, you can only send the 1 track to the connected Bluetooth speakers as best I can see, so they will all play the same tune.
After searching for info, I have at this time to conclude Bluetooth will probably end up like Betamax v VHS etc, Wi-Fi will probably win this battle, simply because it has the greater power\range, there is also the "lag" issue so if playing the same tune, it's getting it played at the same time on each set of speakers, otherwise as you go from room to room you will being getting a case of Deja Vue.
Sonos does appear to be the hands down winner in what you want to do, and it would be the perfect solution for you without waiting for the tech to catch up, they have already got it all in place, and more importantly got it working, and well at that, there are other systems, This Article has a look at that, but you can get Bluetooth streaming hardware, but as I said earlier I would not go this route, not until some future point where it has earned a rep in being able to do this.
There is one last cheapskate\poor mans option is your immediate solution, use 2 devices, connect your tablet to one set of speakers playing one playlist for it's media player, then connect your PC to the other set of speakers, the only thing that may hinder this is if the speakers can't be identified individually, then each unit may struggle to connect, but my logic tells me each device "should" transmit it's own address, and they would both show up in a pairing search, thus allowing you to select which set of speakers to connect to, but once done I suggest renaming the connection so you can identify it easily from thereon, so sorry there is no simple answer, but at least you have options if nothing else, good luck on your quest.