My DS is also four months old. His sleep has markedly deteriorated in the last couple of weeks. He has gone from sleeping through for 10-12 hours virtually every night to waking up several times over a 12 hour period. Fortunately he doesn't cry if he's held and walked up and down. Naps have also become pretty short, which is difficult today when I'm working from home! I think you can't fight what they want to do so no point trying to force them to sleep if they don't want to. Is one of you still on parental leave? Can you stagger sleep with DH to make sure you each get a decent amount?
I'm on leave. my DH is wonderful and always wanting to do as much as possible, but his job is our income and high stress and he can't be going in on no sleep daily. DS had colic and I believe silent reflux. I got a sweep at 42 weeks and wound up with a forceps delivery and i honestly believe that he was truly not ready to come out yet and I selfishly wanted the pregnancy over. (may be silly sounding to some...). I don't think that he would be as difficult if I let him sleep in our bed or held him for every nap, but I'm not interested in that.