Elderberry - firstly congratulations on no.2!
Secondly, I so know how you feel! ds (also 18months) is also going through a very clingy patch at the moment - I'm not really sure if this is a phase for his age or whether it's due to circumstances (dh has just started working away from home during the week when previously he worked from home) - I suspect a bit of both.
I've downgraded my expectations on what I can get done in a day, tbh. That keeps us both sane.
I try and make sure I give him lots of good positive attention (commenting on what he was playing with rather than directing his play, if that makes sense) and try not to give the clinginess and whinginess too much attention (although I don't always succeed in this). Also (although I'm not sure this is a good thing to recommend - I feel guilty enough as it is) I use the television when I absolutely have to go do something, e.g. cook us lunch. He'll still pop in and see me in the kitchen but soon realises it's not as interesting as Bob the Builder or Balamory and soon saunters back out.
As an example, one of the things he started doing was having a real screaming fit and throw things down the stairs if ever I left him upstairs to go and do something downstairs. The absolute last straw was when he threw his milk bottle which came open and I still haven't got the stain out of the carpet!!!
So, I've cut right down on trips downstairs as far as possible (I get up five minutes earlier to get his milk ready for when he gets up) and when I do have to go down (carrying washing for example) I tell him calmly where I'm going. If on the way back up there's toys on the stairs, I pick them up without comment and they go in a box on a high shelf and he doesn't get them back that day. If there's none or if he hasn't yelled that much then I give him lots of praise for his patience, etc. He still hates me going downstairs, but he's getting better at playing on his own for 5 minutes with only slight whinging, the tantrums have all but gone (well for those occasions anyway ;o) ) and hardly any toys get thrown down the stairs anymore - think it's been over a week now since he's done that (I'm sure I'm tempting fate).
Sorry, that's a bit long winded, but thought an actual example might help!! I'm hoping he grows out of this phase very soon though!