I think the egg chosen at the beginning determines the pattern.
One means 3 girls, 3 boys, 3 girls, 3 boys
One mans Boy, Girl, Boy, Girl
One is random
Someone else posted their findings in a thread on here. I think this pattern is restarted when you Marry another Friend rather than date place. Like you say, both babies are the same gender.
The BFF Heart doesn't have to be full. I married two on my first go just by 5 bumps daily until their 'friendship meter' was full (The one listed in the friend list rather than BFF Points).
You can also speed up the process. Yes the Tama's have to be 6 However they only have to be an adult for 52 hours before the date place/Marriage becomes available.
So a TF becomes an adult aged 2. Say it becomes an adult at 12pm on a Monday, at 4pm on the Wednesday it can marry but will only be aged 4 so date place won't be showing. Set the time to 6.59am and wait a minute. When it wakes up it'll have aged a year. Do this twice and it'll be 6 years old and your good to go. Saves you at least a day if you've got a character you don't like.