OK, thank you GreenBay42, I'll try to put the first router into bridge mode if I get there once.
Edit: sorry, I missed to turn on the pptp passthrough. After turning it on the outgoing vpn works fine.
[But one more strange thing: trying to connect to a PPTP VPN from the inside network through the D-Link and the ISP's router. With my previous router (which I replaced with the D-link) it worked without any problem. Now I can't connect through the D-link router. I connected my client into the middle network, right behind the ISP's router and before the D-link, and it also worked. So it seems like D-link is different in handling the VPN traffic than other routers.]