I'm going to assume you're using long sweep wyes and not running 90's....
The biggest problem for what you're doing is mixing the washing machine up with the wet vent. You'll need to tie into your system downstream of the bathroom with your 3" to the washing machine. 3" up to the 90 for the trap on the washine machine, then 2" vent up from there.
For your reference about the washing machine: http://ecodes.iccsafe.org/icce/gatew...orida_plumbing
Go to chapter 9, section 909.1.