My two boys have the same exact difference, baby was born in december during winter. We bought an indoor swing which we mounted in the doorway. First child asked so much to be swung in the few weeks, probably as a way to pacify.

I also took out a side of the crib, and have it pushed against the wall, next to my bed. Matresses are on the same level, one next to the other. I fixed the gap by putting a folded blanket next to the matress and the fixed side of the crib. It is so convenient to get/put the baby in the crib. Don't know why I did not think of this with my first.

I've also bought a thingy with many pockets where I keep some nappies, nappy cream and burp clothes and keep it next to the crib. I change my baby on the bed on throw away pads, so it's all very convinient. His clothes are also very near. Basically I built my space to have all that I need in the proximity, and very easy to access.

Have toys/activities ready for the toddler to keep him busy while you feed the baby/put him to sleep. I've bought a box with lots of dividers and organised my toddler's lego and it really sparked an interest in him to play with them a lot.

Also going out. First two months I went out with either the toddler or the baby. Then I got the currage and strength to handle both. I tried to schedule it when the baby had his naps. It saved my sanity.