New Stepfather Stepson Relationship

My 10 year old son loves his new Stepdad but his behaviour really makes his SD angry at times. I worry this is never going to be resolved and will only get worse if we can't get some help. Problems with my son's behaviour include:
moaning and grumbling about anything he doesn't want to do
trying to debate anything and everything
delays at bed time
answering back
interrupting adult conversation
tantrums
In between all this negative behaviour are a lot of good things too. He is working hard in school, adapting to a new routine quite well, although the grumbles will come. I often choose to ignore the grumbles, but other times I tell him off immediately and warn him if his complaints continue he will lose XBox time for instance. My husband thinks I am too soft on my son, particularly after apologies have been made...I forgive and forget and move on. The behaviour sparks again later.  He doesn't seem to appreciate what he has, and is always wanting the next best thing, another packet of pringles, go to the cinema etc...then when it happens he is still sulky and argumentative. My husband expects to see him more grateful and appreciative. Instead my husband sees my son with an attitude that "nothing is ever good enough!".
My son will be cuddling up to his stepdad one minute then soon after go too far being silly.  He will be told "that's enough now stop it" and my son's reaction is almost like a toddler tantrum, crying, stamping feet as he leaves the room, back chatting etc.  Then my husband says things like "that's it, I'm not doing anything else for him now because he doesn't appreciate it..nothing is ever good enough....." and there is tension again. My husband is working away Mon-Fri for several weeks, and he dreads coming home for the weekend because of how my son may behave. My 4year old daughter has started to mimmick some of his expressions and reactions too which is making things worse. When my daughter acts up my son is blamed for setting a bad example.
Is there any way out of this cycle?  We have only lived in the same house for 6 months now.
Thank you for any suggestions!!