Hi L.,
First of all, kudos to you being an divorced mom and raising twin toddlers. My son is just 22 months old and couldn't imagine trying to discipline and handle the tantrums of two of him.
Second, you son is not unhappy with you--he is just having a hard time with dealing with and expressing his emotions and independence. And though all kids are different and some have a harder time than others, the behavior is not about how much he loves you it is very typical of his age.
Tantrums are not avoidable, esp with a strong-willed child. (just ask my own mother about raising one these LOL). But there are things you can do to lessen their severity.
First of all consistency is very important. Not just with now you handle his tantrums but with his entire day and routine.
Having a very consistent routine with eating, nap times and bed times and even play times gives toddlers and even older children a sense of security (they know what is going to happen next). This is especially imporant with not only bed times but the things you do that lead up to the bed time. (Bath, brush teeth, story, bed--or however you want the routine to go--a wind-down time is important)
The same goes with naps--both nap time and bed times should ALWAYS be within a 15 min time period. If his naptime is at 2pm then is should never be before 1:45 or after 2:15.
Also a well rested child is less prone to tantrums--is he sleeping at least 11-12 hours a night and 1.5 hour or more nap? Again many children are fine without such a regiment, but a strong will child will do sooo much better with one.
If he is not sleeping that long--look at his bedtime and if it is after 8pm move that thing back in 15 min intervals until he is sleeping that long. Yes, an overtired child sleeps LESS and not as well, so moving a bedtime back will actually have a child sleep LONGER.
And at his age, he should be able to sleep through the night--meaning unless he's sick he should be able to get himself back to sleep on his own most of the time. By going to him when he is having these fits, you are only reinforcing his behavior. When he does this...you come in and hold him. If you want him to sleep through the night on his own, then you can't undermine yourself like that. For a "plan of action" to address this issue, please check out the Baby Whisperer book I listed below to help out.
I can't also think that something about your divorce, whether it be the disruption, the time he spends with his parents, or some sort of inconsistencies there are also worsening his behavior.v So look at those things too, and if your ex has partial custody make sure there is consistency across the board.
So many things can be done and looked at to lessen this behavior that I couldn't possibly get it all in one response, but I would really like you to check out the following book:
Secrets of the Baby Whisperer for Toddlers
http://www.amazon.com/Secrets-Baby-Whisperer-Toddlers-Tra...
She has wonderful insight and ideas how dealing with different personalities in toddlers.
Finally, don't give up! You CAN do this. Get a plan together (whether it be from advice from a mom , a recommended book or a professional) and stick to it!