My LO is so sensitive

I feel your LO cries because to draw attention. They like to be the centre of attention all the time.
My son is 28 months now and he comes running and sits between us in the sofa. If we are talking, he tries to move my face to look at him.

Its all a passing phase. Just try to balance out the times when you give her the attention and tell her a NO saying mommy is talking right now, will get back to you in sometime. And do give her the attention after a little while. That way she will learn the difference and stop crying to get your attention

 

your LO will understand what you are trying to say if she is in the other end.. have you tried doing a role play.. like when you and DD laugh while playing, ask your DH to pretend to cry in front of you both suddenly.. saying mommy and daughter are making fun of daddy.. you tell to your DH in front of your DD that 'hey we are playing and laughed for this n that... common, we are not laughing at you..' tell DD to console daddy saying 'dont cry daddy.. we are only playing.. if you cry, you will be called a cry baby..' even if she cant say it on her own.. you say it to her and let her repeat. repeating this a few times will make her get the feel of it.

 

Hey I second AD's idea, best way to make them realize. I've done this with DD for several things like pretending to cry while washing hair, wake up time etc, etc.......and it worked wonders....
All the best, this is just a stage!

Uma