Hi Tarsh,
What time do you get in? Have you paid for transfers or are you planning on catching a taxi?
Siam@Siam is well located to access the main shopping district. You will be able to walk to the MBK shopping complex which will be a good thing to do on your first night. There are 2 great food courts there, one offers very cheap reasonable quality food and the other is a bit more upmarket. The shops at MBK offer much cheaper pricing than some of the street markets without the hassle of too much hard core bargainning. You can still haggle a little but many prices here are fixed. Dont buy too much on the first night as you should probably wait until you go to Chatuchak Market. You can do this early on Saturday morning.
Getting to the market is easy by the skytrain. Your closest station is National Stadium, which is the end of this line. From here, catch the train one stop to Siam. You will then change trains which is as easy. Board a train heading for Mo Chit. This is, once again, the end of a line so you will not miss it. Just follw the crowd, as 80% of people that get off here will be heading towards the market. Dont eat too much at the Hotel buffet as some of Thailands best street food will be on offer here. Get a market map at the Tourist Police booth near the entrance...you will need it to find your way around. Plan on spending most of the day here if you like to shop.
If you want to see some temples and experience some of Bangkoks culture, consider getting a guide on Sunday. I would recommend contacting
Bangkok Guide - Tour with Tong in Bangkok. It is easy enough to do it on your own, but as your time is so limited, you will get the most out of the experience this way. A morming with Tong or one of her guides is like being shown around town by a good friend. You and your Mum will have a blast. Tell them what you want to see and they will tailor a tour around you. They will also drop you off at the airport to meet your plane to Phuket. Hopefully, your flight is late in the day.
With only 2 days, I wouldn't try and see anything out of the City as you will spend too much of your precious time travelling.