my girls are exactly two years apart, so i do know what you're going through! and no, you are NOT a bad mommy!!!!! if you were, you wouldn't be here! my girls are now 4 and 2 years old and they play together really well, so just know that there is light at the end of the tunnel!!! i remember all the months i spent reassuring my oldest that someday her little sister would be big enough to play with her! she even reminds me that her baby sister used to be so tiny, but now she can talk and play!
it's fairly common for older siblings (especially at your child's age) to regress when new babies are introduced into their world! suddenly mommy and daddy and everyone who visits are completely awestruck by this tiny squirming little screaming baby and the older child feels threatened by it.
a few things you can do to help your older child adjust.... you can leave the baby with someone you trust (daddy, grandma, whomever) and take your older daughter out on a special big girl date to somewhere fun. really stress the "big girl" part a lot..... "you get to come with mommy because you are a big girl and baby has to stay home because baby is too little...."
let her help you with chores around the house. she's big enough that she can help get the laundry out of the dryer, she can help wipe the table after meals, she can help set the table, she can even help unload the dishwasher (plastics, silverware - just make sure the knives are all out first!), you can even let her "cook" with you (stirring stuff, beating eggs, etc...). again, all things she gets to do because she is a big girl, and baby can't do it because baby is too little. really praise her for her "help" too, and emphasize that she is a big girl and baby is a baby, and what would you do without your big girl helper???
let her help with the baby. baby is so little and can't do anything right now, thank goodness baby has a big sister that will help take care of her so that baby can grow up and play with big sister.... let her get the diaper changing stuff out for you, let her get out the burpies, baby's blanket, baby's binky, etc.... you can even let her help you with bathing the baby. she can use a cup to pour the water on baby's tummy to rinse the soap off....
let her have her blanket. she needs a comfort thing and if the blanket makes her happy, it's not going to hurt anything to let her drag it around. we leave ours in the carseat when we go to the store because we don't want it to get yucky sick germs and have to get it washed as soon as we get home (it takes me forever to get the laundry going, so i think my two year old has taken that into consideration!!!)!
as far as the binky.... there are several methods you could try to get rid of it all together, but if you do it too soon, there's a good chance she'll just steal baby's, so you really want to be sure she wants
to get rid of the binky first....
i waited until my older daughter was around two and a half to get rid of her binky, so this method could really work for you. we went and looked on-line at pictures of really bad teeth. black, rotten, crooked, nasty, gross, disgusting teeth (i just looked up "bad teeth" and went to the images). i told my daughter this is what can happen if you have too many binkies. then i asked if she wanted ugly black crookedy teeth or beautiful white sparkly princess teeth? she chose princess teeth and so i said then we can't have too many binkies anymore, okay? she never took a binky again. funny thing was, my goal was just to get her to leave the binky in her bed and only have it at naptime and bedtime! but she did NOT want ugly crookedy teeth and she got so offended that i even tried to offer her a binky that day at naptime!!!
until you think she is ready to get rid of it all together, you might get her a special "binky box" she can keep her binky in when she isn't in her bed. let her put it in first thing when she gets up and then put it up on a shelf so it will stay "safe."
as far as awful winter weather hindering the outdoor play.... i so understand!!! we have a folding slide that i got at babies-r-us and it's been a life saver!!! it fits perfectly in our hall closet next to the vacuum cleaner and on bad weather days, i pull it out and let them go nuts on it! i also got my girls a little pop up tent that is easy to fold and put away when it's not being used. it really helps keep them busy!
i sure do understand the not having family around. our closest family is a good eight hour drive away, and most of my friends here have kids too, so it's hard to feel like i can just leave my kids with them (we do swap a lot though). joining a mommy group or a play group really does help! our play group was started through our church, and i know at a few elementary schools, they have play group sign ups too, so those are a couple of places you might look too.
anyway, sorry for the rambling. i just really know what you're going through and these are all ways we dealt with it. hope it helps!