Congratulations mommy! I am so happy for you and your husband. What a challenge a baby would be at 44 and here you are with two of them. I had my last one at 36. What a joy she has been! I had two others to practice on before her, however.
You didn't say how long your son has been off of oxygen, but I am inclined to agree with you that this is a learned behavior that is just going to take the patience of Job and continued consistency. I cannot stress consistency enough. Give in one time and you're back to square one.
You said you don't give in to him until he quits crying or at least fussing. If I'm understanding you correctly, you're saying that he eventually gets whatever it is he is fussing about. Does he always get what he wants depending on his actions? Young as your children are they learn very, very quickly so I would recommend you and your husband decide what is and isn't important to you when it comes to what the children can have/do. Establish rules and consequences now. That may sound a little silly when we're talking about a 20 month old, but trust me, you are training him every second of his waking life. Why start out one way only to have to retrain him when he is older?? That just sends mixed signals to a child and tells them that mommy and daddy really don't know what they want so if I am patient enough and try enough tricks I will eventually get my way. Does that make sense?
It is also very important that you and your husband are on the same page when it comes to how you want your children raised and disciplined. If you aren't supportive of one another then the children will pit you against each other.
Hope this helps. I'm a first time grandmother so I've seen it all...lol. My grandson is only 2 months old but he already knows what he does and does not like and he lets you know it.
Keep up the good work and enjoy every second with your two little (soon to be big) blessings.