I'm having a weird problem and hope somebody can tip me, what way should I dig to.

I'm using MacBookPro with Lion 10.7.3 both at my working place & at home. 

At working place, we have a domain-based network with 802.1x authorization (more than 400 computers) and to connect it I'm using Ethernet cable. IP range is 10.10.2.*. All network settings are setup automatically by DHCP. Also, in settings, I have Network Account Server setup in the User&Groups Settings for my work Domain server - and it is available only from corporate network.

At home, I have an ADSL router, that shares Internet connection by WiFi in NAT mode. I'm using WiFi to connect it. Router gives out addresses from 192.168.1.* range and all settings are also set up  by router's DHCP.

So, my problem is the following. When I come back home from the office, I open my MacBook and AirPort automatically connects my WiFi network. After this, for about 1 minute I'm able to browse sites & ping hosts successfully. But after this minute, network connection is broken down. All pings return time-out. trace route to google.com stops on 192.168.1.1 (which is my router). This lasts for 3-4 minutes. After that network connection is automatically repaired and all pings go smoothly again. At the same time, when my MacBook return timeouts, I can successfully ping any host from my wife's MacBook - so this doesn't look like router issue. When I come to the office, I don't have any issues and Internet connection is available & stable moments after ethernet cable plugged in.

Do anybody has any clues about this? What should I monitor & what settings look for resolving this issue? 
Please, ask, what additional information should I provide.

Hoping for good advice & thanks in advance!