D10 controller providing OJT experienced a loss of separation when late frequency changes and failed instructions to stop subsequent aircraft at lower altitudes resulted in multiple separation events.

Narrative

Aircraft X departed DAL. It is normal to climb these aircraft on runway heading and hand off to DR2/3 and top the DFW traffic climbing off Runway 35/36. Aircraft Y was still not on our frequency at about 4 NM off the departure end of runway. My trainee called DAL and asked them to switch him again. Aircraft Y checked on level at five and starting his right turn northbound as per the published SID. My trainee told him to fly heading 310 and climb to 080 as per the common practice. Unfortunately Aircraft X completed his northbound turn before starting turn back to heading 310 and did not start climb right away. I called down to DR 2/3 and told them we got Aircraft Y late and turning him back to 310 and climbing him to 080. Although I did not tell DR 2/3 to stop his two DFW departures at a lower altitude; this is what I implied. We switched Aircraft Y to DR 2/3. A mile or two later he checked back in with us; he did not flip the switch. We told him to expedite climb and switched him again. DR 2/3 stopped his first DFW departure at 050 when he was out of 042. Air Carrier Z however climbed up to about 053 when Aircraft Y was just thru 060; first deal; then DR 2/3 stopped Air Carrier W below Aircraft Y but he too was within 3 mile with less than 1;000 FT. Recommend changing DAL and DFW SIDS on North flow to simulate how we run traffic.