Hi, A.,
I have a three month old and he is also very similar. It is what it is! You can't really MAKE them sleep longer if that is all that they are needing. My three month old may occasionally sleep for 2-3 hours at a stretch, but mostly it is 30-60 minutes at any given time and then maybe even 10 minute catnaps throughout the afternoon, so it never really feels like he sleeps at all from around 3 PM until 10 PM. I just put him on his play gym and he plays there for a while and then I move him to a bouncer and then to his swing. That is how I survive. I have a three year old as well, so I can't just hold my little one all the time. Most of the day he has to just hang out on his own. I would suggest the same for you if you need to get things done. Just put him somewhere where you can see him, but where he can entertain himself (such as a baby play gym on the floor) and then do what you need to do. Put some music on for him. Or let him play in a play pen. My baby cries all evening about once a week, because all he wants is to be held, but I can only give him 10 minutes at a time, since I have to cook dinner, feed my three year old, etc., etc. and I am alone in the evenings since my husband works then. So my three year old and I just have to learn to listen to my baby cry some nights and just keep talking to him and holding him intermittently. Most other days, though, he is really good. Don't get discouraged that your baby doesn't sleep for longer than 45 minutes. His patterns will change over time and for now, just try to figure out how to get things done even when he is awake. They don't need 100% of your attention just because they are awake. Both of my boys learned to deal with me working from home on the computer from birth. Now my three year old is very independent and my 3 month old is, too, when it comes to playing without me there. Good luck and enjoy this time!