Hi,
I'm a single mum of two and your situation is identical to mine ; a brief renunion also resulted in baby number two! I have a 3 year old and a 9 month old and no longer live with their father.
Although I have now relocated to be closer to my mother and siblings for support, I can't stress enough that it's vital to do this if you possibly can.
Having one baby was logistically bearable, as I did get mental breathers when she napped during the day and I used to just take her out in the buggy when I needed a break.
But with two, suddenly the logistics are more challenging. I can't just nip up to the loo for instance without first doing a recce of the room they're in, make sure toddler's ok, baby's ok, nothing's going to fall on them, toddler isn't going to bounce on the baby's head, etc. during my brief departure!
Also, (I don't drive), gettting two young babies into town on the bus can be a nightmare unless you havbe a good double buggy.
Certainly the blissful moments of togetherness you get as a mum of one, when you can nod off on the sofa when your baby does, will not happen with two! - they will not neccessaruly want to nod off at the same time!
If you're the kind of person who could enjoy the intense challenge and total selflessness required and be prepared not to have time to barely flick through a trash mag for the first year after baby number two's born, you'll be rewarded with a life-fulfilling sense of achievement and a feeling that you've become invincible, that anything's possible now you have managed to do all this on your own.
But having support, whether it's extended family, reliable friends, or regular pre-school dates, playgroup sessions, or dropping in to a Surestart centre, is vital. My mum takes my 3 year old to playbarn once a week and then looks after her rest of the day, so I get around 6 hours to myself on that day. That's enough time to concentrate 100% on the new baby, have a home pedicure (do it yourself or have a mobile beautician around), catch up on Facebook, get some major chores done, read a book or magazine, etc etc. Basically have some peace and quiet. If you're lucky, new baby will nod off for a few hours too, then you'll have lots of time solely to yourself, .... but you may not know what to do with all that time!!
It's possible to cope, it just requires mental committment to a bigger challenge than your used to with one child, and a support system.
Your two children will be rocks for you once they grow up, and what a wonderful role model you would be for them, inspiring them to the same integrity of character and gung-ho attitude you will have shown doing all this by yourself. No man could cope with this sort of multi-task!