Dear elders,
I am in a 3 way split over what to do. I basically want a DLSR that will give me good portrait shots(with blurred background) , a camera that takes clear shots in low light/ indoors with uplight lampshades situations and take photos of my kids playing with photos as blur free as possible.

The 3 cameras I have whittled it down to are : CANON 1100D , NIKON D3100 and PENTAX K30.

I like the idea of remaining with a compact and this keeps bringing up the SONY RX100, but I am hesitant about Sony as the others are three of the biggest names and they always have been. This coupled with my limited knowledge of sensors and finding out that the DLSR's have bigger sensors, so they will/should produce much better lowlight photos.

The issue I have with the Canon is the lack of stabilisation , I seriously don't want to spend 350 to find a camera that blurs photos with minimal handshake.

The issue with the Nikon again the IS and long lag, the bonus is the self cleaning sensor.

The Pentax, well that ticks boxes, but this time it's the weight. I have only ever used a P&S.

Obviously the Pentax poses less issues, but i don't want to buy it, love it but leave it in the cupboard because its weighing me down

Any advice would be greatly appreciated.

Thank you