I have so been in similar situations after my dd2 was born! (similar age gap).
I think what I learnt with time is to drastically simplify anything in my day. I started off by never assuming that the baby would have a good nap, so would not embark on an extended activity that required a lot of input from myself with dd1.
Your eldest girl probably just wants to hang out with you, feel you near her, feel that you enjoy being with her. That doesn't have to go hand in hand with an 'activity'.
After having many experiences like the one you describe above (we live and learn!) I ended up just putting on a dvd and sitting next to dd1, or getting out some colouring (can still be done with baby on lap or breastfeedng) or playdough.
Then if baby woke up screaming (she was a terrible napper) I would ask if dd1 wanted to come with me to get her or wait for a bit and let her decide. Then bring baby downstairs and say something like 'Oh this baby is so naughty doesn't she know we just want to colour?'
Sometimes dd1 would defend the baby 'she's just a baby' and sometimes she would give her a withering look!
I make it sound so straightforward.. But the phase you are going through is a bloody nightmare! I remember it being particulary had from the baby being 3 months until about crawling and babbling time in terms of coping with eldest.
There really is no right answer. It may help just to know that others have been there, have lost it unfairly with oldest child and know that it will pass. (eventually)
BTW mine are 4ish and 2ish now and it's all so much better now. (Seems like a long way off to you probably, but really it isn't)