First of all don't feel like you have to interact with her all day. gosh my 2 run all over the house together and separately (i can have the 3 of us doing our own things sometimes in 3 different rooms) for ages - i just let them get on with it a large part of the day. some things we do together though are:
playing with blocks - liv is 14 mo old and can build a tower of 4-6 blocks and enjoys that and knocking down bigger towers built by me or her big sis
tea parties and pretend cooking - we have plastic cups, teapot, plates, spoons etc and play food and liv likes to stir things and "feed" me with a spoon. these things get played with every day and can be bought cheaply (don't need fancy sets)
plastic animals - we make animal sounds and make them "walk" or "gallop" etc
outside play - ride on toys / pushing her around; swing and slide, just rolling around on the grass, playing with leaves and flowers etc
just being there for her to show things to me - she is doing the playing but i react and give verbal narration to the events (like the pp said about pointing and naming for them)
balls - she loves all balls and we have about 6 or so balls of different sizes and textures and she is really loving practicing throwing - not able to catch yet but throws balls (and other toys
) all over the house.
musical instruments - we have a basket full and i get them out and we all play different ones and just go nuts
we do watch DVDs together every day - i gave up on that a long time ago - my girls both really like them and i find that alex learns a lot from them and Liv is exposed to them because of an older sibling. she will come and go though so i don't worry (too much
). i do think it is something you relax about with 2nd children as it is a part of life usually.
i guess part of why she plays on her own a lot is because i am not precious about the house. we have MANY toys and stuffed animals etc out at one time (yes my house looks like a mess for much of the day
and my girls tend to flit about according to their moods and if i notice a bit of boredom hapening i will direct them to something like the music or put on a CD for us to dance to. i let her climb on the furniture/sofas too and have a small kids sofa she will retreat to to chill out and play quietly. Just last night my Dh was saying that if i want to be more productive for the house or myself i really don't need to be interacting with them all day
I said to him what i said above - a lot of the day i am just "around" or doign the busy stuff to organize them (their food, laundry etc) and playin with them in short bursts. kids learn a lot on their own and it is actually best to introduce a toy and let them just explore it on their own and try to figure out all the bits - intervention is only "necessary" when they are asking/indicating for help or if it is something you enjoy doing with them and want to participate on their level. HTH