Great responses here....
I would also wonder, HOW your 3 year old sleeps when at his Dad's house??? What is the arrangement there, or their "routines" at night & their sleeping arrangements? Is he wandering around there too, in the middle of the night? Is he able to co-sleep there too, if he wants? Or does he have to sleep by himself? DO they have a REGULAR bedtime at his Dad's house or do they go to bed "whenever" and late? Does your 3 year old nap there? SOMETIMES... when there is a youngest child among many older children... they get, by default, ending up having to be on the same "schedule" as the older children... even though it is not age appropriate.
ALSO, what about TV shows? Is your 3 year old just being exposed to things that ALL the other older kids do.... even though he is ONLY 3 years old? Even a 'scary' TV show can scare a young child and/or stress them out for example.
-- I would see what kind of things your 3 year old is 'exposed' to at Dad's house. He IS the YOUNGEST of all the children... and he can't just be doing the same things as them or watching the same things or having the same play/sleep routines. Do you know what I mean? This can also tweak a young child...
-ALSO, well, you have an "un-official" Boyfriend in your home too... And, I'm sure, this affects your 3 year old, because he is in your bed too with "Mommy". And, maybe he feels displaced... and no where to go himself. Even if he goes in your bed to co-sleep with you, well, the Boyfriend is there. Personally if I was a little kid, I wouldn't want to sleep with Mommy "and" a boyfriend... unless he was my Daddy and I had a normal/good relationship with him. A child... co-sleeps for comfort and security... but, that has been changed for your 3 year old. EVERYONE in the house has a sleeping 'habit'... Except HIM. Your older sons are old enough to sleep on their own, Except him. But he actually has NO place to sleep... when he needs comfort or security or simply having night-time fears... its like playing musical chairs, except that your 3 year old has NO chair to sit on because they are all taken already.
I think, that the "every other weekend" at his Dad's house, is kind of a LOT... of having to switch gears for a young child. Can you yourself imagine, if you had to literally move house every other weekend? Would you sleep well that way or feel secure and settled? I know I wouldn't.
PLUS, at his Dad's house, there is a live-in Girlfriend, with her own son. HOW is that relationship? How is your 3 years old's "role" there and what is the "pecking order" in light of that...? Does the Girlfriend embrace/love your sons too, and treat them equally??? Does the Girlfriend's 6 year old son... integrate well with YOUR boys and visa versa? Do they ALL get along normally/well together? (ie: Dad, Girlfriend, her kids, your kids?) Is the situation "normal" there? Is it like a family? Or are the boys left to just amuse themselves? Any behavioral problems there? Any stresses/problems/unfairness/questionable living arrangements there? I would examine those things... or ask your older children....
Next, as the other poster said... ask the older kids how they feel at the Dad's house. Everything ok? And with their 3 yr. old brother? MAKE SURE you keep open communication with your eldest children... they will be your "beacon" or your source of keeping tabs on their well being, since they are always every-other-weekend going over to their Dad's house.
ALWAYS encourage boys, to express themselves... especially to you, their Mommy... you will be seen as their "soft place to fall" for anything... good or bad.
For your 3 year old, it could be simply a security thing... and he goes back and forth to unconsciously make 'sure' everything/everyone is 'still there.'
Also, try teaching your 3 year old the names of 'feelings' and perhaps... even teach him a special certain word or something, that he can tell you anytime he isn't feeling happy or if something is bothering him. That way, he has a concrete "word" to tell you and convey that to you. It would be like a code word.
And yes, certainly ask your eldest children if your 3 year old is having trouble sleeping at Dad's house too. And if they have any ideas why? ALSO... I would encourage your eldest boys to understand that they need to 'help' by watching over their youngest brother... looking out for him, and being good brothers that way... (are your sons close?) That way, your 3 year old may feel more 'secure' when he is at Dad's house... and that he fits in and has a CLOSE 'security' there too... that he can also 'rely' on his brothers kind of thing. Teach your boys to have each others back, so to speak. I think its important if/when siblings can look out for each other... especially when they are away from home and you...
Lastly... I would DEFINITELY ask your Ex, how your 3 year old is, at his house? Ask him all the questions you can, and tell him that your 3 year old is having sleep problems... and if he knows why or anything he can shed light on.
All the best,
Susan