Travelling with two passports

[ping26]

Here is my Story;
I'm a Family member of an EEA national, my wife not working since more than a year and this is because we have a 1 and half year baby to take care of.

I have changed my name a while back from Example "John Smith" to "Michael Smith". now I've changed my passport too so my old one which hold the EEA residency is now cut on the corners of it.
transferring the residence to my new passport will take around 6 months and I will have to buy a health insurance for all my family members (around 800£ for 6 months) as she is not exercising a treaty right now (I'm the one working for my family).
I wonder if I can travel with the two passports abroad as I have only one year left for me to apply for the Permanent residency here in UK?

[Directive/2004/38/EC]

Duplicate thread! http://www.immigrationboards.com/viewtopic.php?t=111861