I too use a closed bottle and shake/rock the bottle - I use a 5L bottle, so the initial 3.75L of water has plenty of room to churn and thoroughly mix
However, 2F/2F & Anscojohn are right, shaking it gets a lot more oxygen into the developer, so it won't last as long if you intend to store it.
I leave my developer to stand for at least a day before I need to use it, do a batch of films and pour the rest away (its not worth keeping and taking a risk the next time I have a batch to do)
Like 2F/2F, I mix my developer a little warmer (45C ~ 110F), as I find it mixes more easily.
Some batches do seem to mix more easily than others but cannot figure out why.
It is very important to get all of packet A dissolved before adding packet B.
I have never had my developer powder form clumps though, its always poured out of the packets in a fine powder and stayed as fine crystals in the water.
You need to break those clumps up if you want to get them to dissolve in a reasonable time frame
You have a few of choices :-
1) Break up the clumps - big lumps dissolve only slowly
2) Warm the developing solution a little more (stand your bottle in a bath of even warmer water - but not too hot - 50C max)
3) Keep going with moderate agitation, it will almost all eventually go into solution
4) Junk this batch and start with a fresh packet
5) All of (1), (2) & (3)
Good luck
Martin