Hi there TFT.I reads your OP and came to the bit about new baby and thought "Aha I've been here!!".It sounds as if this could be the crux of the problem.I only have a 2 year age gap between my 2 and those first few weeks/months are really really hard.The eldest is (understandably) a bit put out by the new arrival usurping his attention.DS was terrible for the first few weeks and VERY attention seeking despite attempts to prepare him for the new baby,somewhat optimistic on my part as I was not prepared myself for the sleepless nights plus baby plus toddler!!!
Firstly,and most importantly GO EASY ON YOURSELF.
If you can get a cleaner/ignore the housework as much as possible/get your nearest and dearest to help.
If your little one attends daycare then try to maintain their routine there as much as possible.I found the 2 days without the eldest gave me some opportunity to just concentrate on me and the baby.
I found that the mainstay for the first few weeks was c-beebies and reading books to the elder whilst bfing.To be honest I was so tired my usual strict rules re tv went out the window!!!
I also found that getting dp to look after the little one and spending time with the elder even if just for doing bath and story at night gave him some much needed one to one.Also I occasionally left the baby with dp and went out with the toddler on a weekend morning for 1 to 1 time.
Finally,although it doesn't seemlike it when you are in the middle of it it DOES get better with time,the elder WILL adjust and as the little one gets older will have a fascinating playmate.Do not feel guilty if you have some wobbly "Oh god I am a terrible mother as I lost my rag" days,I do not think anyone can be even tempered all the time in those early weeks unless you are a saint or have a wonderfully good sleeping baby.(I didn't as you can probably tell)
Look after yourself,as it is very easy to forget the most important person in all this when you are dealing with a toddler and newborn and that is you,as you are the one who provides and nurtures the children for 24/7 and you need some time too.