i have a bad news for you:
you actually can share resources from computers on different network segments.
obviously performance of it will depend on the protocols and requirements. access to network shares via windows networking will be quite slow on typical adsl line, but still usable.
what you need is a vpn between offices, and static routes added on the edge routers in both [or more than 2] locations. you can go for standardized ipsec solution and use hardware/software provided by many vendors or you can use openvpn which does great job for me for last 6 years or so.
so an example - technology / vendor agnostic.
full image here.
computers in office A use r00 as default gateway [and nat router, and dns machine and maybe even dhcp server probably]. they send all packets to hosts they cannot reach within 10.0.0.0/24 to that machine. similarly computers in office b use r10 as the gateway.
r00 has a default gateway pointing to the internet service provider and additional static route telling that networks 10.0.1.0/24 and 10.0.2.0/24 can be reached via vpn. this vpn can run locally on r00 or on separate box [here r01].
r01 is using your internet connection at the office [ this part was omitted in desperate attempt to make picture a bit readable] to establish encrypted tunnel to r11. r01 forwards packet received from the tunnel to r00 and received from r00 to r11.
r10, r11 do analogical job.
now your 'road warrior' - person sitting at Starbucks and wanting to access some internal resources [exchange server? file server? intranet web page?]. she is using available internet connection to establish encrypted tunnel to your vpn concentrator [ can be separate box or one of r01/r11 ] and depending on the company policy either sends all traffic via that box or just traffic destined to 10.0.0.0/24, 10.0.1.0/24, 10.0.2.0/24. as you see 'road warrior' gets ip address from different range - 10.0.2.0/24 - one allocated to 'dial up' users.
ps. this is a simple case - you can get things more complicated [ and more secure ], but i hope this gives you the idea how things can look like to achieve what you need.