How to connect to remote udp multicast if I have an IP address where the service resided (say 70.70.70.70), the multicast group to connect (say 224.25.25.25) and port (say 2020)?
I use ACE framework and in the sniffer I see that ACE sends IGMP packet to 224.0.0.2, in order to join a group, but my home router (checkpoint) doesn't know what to do with it.
Routers are rarely made and configured to support resending multicast packets to other networks. In other words, multicasts usually work only via one subnet. In most cases multicast over internet is based on establishing TCP connection between peers and sending messages using some transport on top of that TCP connection (look for information about message-oriented middleware).
If you have some particular server, which welcomes you to join to it's multicast, maybe you can provide more details about what this server offers and what it needs to be configured.
I've only seen multicast work on local subnets, so a good first test is to setup the multicast service on a local computer, and see if that works. I've never had success getting multicast to work for remote services, only places where all routers can be controlled, like behind a corporate firewall. Seems like it should work, and I'd like to see examples of the general case working...
You need IP tunneling, a basic VPN service would work but you might need multicast routing above that depending upon your configuration. Wander over to serverfault or superuser for more help.
I have an IP address where the service resided (say 70.70.70.70)
You don't need that.
the multicast group to connect (say 224.25.25.25)
You need that. You need to issue the join-group operation using that address.
and port (say 2020)?
You should have a UDP socket listening at that port.