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One other strategy you might try for awhile is eating your evening meal early and going to sleep as soon as your OH gets home from work. Let him take care of your older child and feed the baby expressed milk.

Then when he goes to sleep, both of you sleep until the baby wakes you up for another feed. Then you can feed the baby and sleep again. If your OH is home by 6pm and goes to sleep himself at 11pm, then you could get at least 5 hours of uninterrupted sleep, and perhaps another 3 after a middle of the night feeding. If you can work the timing so your OH is feeding the baby at 10:30pm, the baby may sleep till 1 or 2 am, giving you 7 or 8 hours of sleep.

Or if you have a relative nearby that would help you, another strategy is to have them come to house and take care of the children at night while you sleep. And they sleep too when they can. Then they go home in the day and sleep some more at home. They can either feed the baby expressed milk or bring the baby to you just for feeding, but do everying else the baby needs at night.

I think that last post was a VERY good idea.
Also just a couple of thoughts/experiences/points
Be carefull expecting a bottle will make your baby sleep, a lot of people find the oposite when combining with brest feeding as it fills their tummy and takes a long time to digest, leaving them feeling bloated and uncomfortable ( think christmas day afternoon!!)
Some children have alergies to formula milk, we have experienced this and it nearly killed me as a vegetarian to find that my baby now had a lactose intolerance servere enough to prevent me from consuming milk products because some of it was passing through my milk. (I became emaciated as I just couldn't consume enough calories etc) actually colapsed on the health visitor while they weighed her!)
Try the NCT They really are very good at what they do, their breastfeeeding councilors have undergone university accredited qualifications to provide them with the skills to help people in exactly your position.
Just a finnal note on formula, Please Please don't use any from Nestle (If you don't know why please just ask and I will be happy to explain) and although it usd to be recomended for sensitive tummied babies Goat milk has now been proven not to be nutritious enough for babies (again see the NCT for more details)
Good luck, You really are not alone, I remember it all three times, I thought it would never end.
I found saying yes to help offers really helped as well!