I think it depends on the cause of the fight. I don't agree with anyone throwing themselves to anyone's mercy. But if you were being overly harsh, or picking a fight and maybe he is stressed and worried... then maybe try talking to him and if you feel the need, apologize.
Do you want him there? Do you love him? Do you feel maybe a short break will do you good? Maybe he just wants to know he is loved and wanted around too, especially if you are fighting a lot. However if he is just being mean or overly harsh than I would let him go.
BUT that is just me.... Everyone is different. You need to do what you feel is best in your heart.
If you really love him then try and have both of you sit down and talk but without fighting i know it can be difficult but do it for the sake of your daughter and your little one thats on its way... being in a relationship is tough ofcourse but if you guys really love eachother you guys have to understand that leaving eachother everytime theres a problem nothing will get solved that way cus thats always the easy way i use to be that way too i been with my hubby for 8years and at the beginning I would leave to my moms house everytime their was a fight between us without realizing everything that was getting damaged around me like my kids that i was dragging with me and i was hurting them w out even realizing it...
My only advice is that if you really love em and think you guys can work it out then dont let him go u guys gotta think of the good time u guys have had and not throw all that just over a fight well thats my opinion goodluck :)