My dd1 was 4 when dd2 was born - it's bollocks that it's harder when the younger one is mobile, by that time they are fun and interactive and can join in things, not to mention they're probably only napping once or twice a day and the older one has got used to them being part of family life.
People trying to make you more miserable by always referring to some nebulous "future time" when things will be worse whilst you're going through a hard time really fuck me off.
It is a tiring time - you try to do so much with your older one to make them feel secure, loved, valued etc that you don't get to 'sleep when the baby sleeps' etc. But it gets better quickly, and absolutely don't feel bad about increased screen time whilst you need it. If your 4 year old isn't at school yet, then structuring the day will probably help, e.g. off to the park after breakfast so older ds can run around whilst you wheel younger ds around to get him to nap, then snacks/picnic on a rug, then walk home for half an hour of tv and a coffee for you, then a table activity before lunch etc etc. I shamelessly told dd1 that we were doing things that she liked because she was very important and the baby didn't get a say. I didn't think dd2 would be psychologically damaged by the conversation given her overriding interests of sleeping, eating and blowing raspberries at the time, and as the situation became 'normal' that level of reassurance stopped being necessary.
It gets easier all the time - first when they reach 6 weeks and start to understand nighttime a little more, then at 3 months when they reach the end of the third trimester and start to interact with the world around them, then at 6 months when they get into a nap routine and have sitting/turning over/crawling thoughts, then at 12 months when they get a bit more ambitious with movement/communication. DD2 is 18 months now and they can actually play together, to a certain extent, and it is lovely to see when they do. It has also done wonders for DD1's patience 
Hang in there, newborn, sleepless, and with a massive upheaval to DS1's world is the hardest bit, it does get easier soon.