Hey there, slings are wonderful
Ok so I know that Tracy said to start as you mean to go on, and it's certainly not too early to start laying some good foundations, but in order to get things done and spend time with your older LO, slings really can be invaluable. What we did with DD was to let her have all naps in the sling at that age, except for just one - for us it was her third nap, since that didn't clash with preschool drop-off or collection. I'd let DS have screen time then (not that you have to do that, of course, but don't feel guilty if you do end up resorting to that - it's not for ever and plenty of us have done it!), whilst I worked on getting DD to sleep in her cot using shh pat. I also used shh pat at BT, since DH was generally home by then so I wasn't leaving DS alone. Shh pat can be used right from the start, you can even use it as LO falls asleep and even into deep sleep if necessary at first, but I'd start by seeing how little you can get away with, you might be surprised
And don't worry if progress seems to be slow, eventually you will be able to do less and less shh pat until she's falling asleep without your help.
What we did is that around 4mo, when the A time was a bit longer and it actually became practical to have more naps at home, we switched things around and she only had one nap in the sling (so DS could go to the park) and that allowed us to be more consistent with sleep training, that's when she started making much more progress and I didn't have to help her so much.
Have a read of this, if you haven't already:
Shush-pat - How to