You are most definitely not alone! I too have a 3 year old and a 14 month old. And while in some ways it is getting easier...it also feels like it's getting harder. Both DC have never been good sleepers, and while at least DD is sleeping through (she started at 2.5 when the baby arrived, typically!) she still of course has unsettled nights. Which would be fine...if it wasn't for the fact she's passed the baton on to her little brother whose sleep is terrible. My DH and I take it in turns to co sleep with him. I'm used to not getting much sleep but I work 4 days a week and it is very hard going at times.
DD is a typical 3 year old. Spirited, developing fast with her language and skills but frustrated that she can't do more. Very stubborn. DS is into climbing up everything, he never stops from the minute he wakes (usually at 5.30am) and likes constant attention. I adore them both and know that they are just doing what babies and little kids do...but my patience is constantly stretched. I do worry like you that my reactions to getting stressed are affecting her.
Every day feels like a constant treadmill (set too fast) of chores, work, feeding, bedtimes, planning meals etc and repeat. We have no family nearby and friends can only do so much (we don't feel able to have babysitters outside of immediate family for both of them yet. It wouldn't be fair on anyone else!) We have very limited rest time and romance moved out of our house a long time ago 
I will say that when I stopped breastfeeding DS at 12 months, it got a bit easier for me because it meant DH can do nights too now. That is an enormous help and gets me through.
What else works? Exercise. Going for a run, not to get super fit but to clear my head and get me time. I am lucky in that I can go to the gym at work, but on mat leave I would go for a 20 minute run once DH got home, or at weekends. It has kept me sane.
I felt no guilt stopping bf because DS was 1 and eating very well. And I didn't have to give him formula which he never took to (or bottles for that matter). The end will be in sight there, please don't feel it won't change because it will.
Much sympathy and understanding to you. Small children are HARD WORK. I wouldn't change a thing but I do occasionally wonder how much easier it would be if we had stuck with one DC. But I know hope it'll all be worth it!