It's impossible, you can't go to Syria having a track of being in Israel (visa) in your passport

Syria will not allow you to enter even if you are entering from another country (totally impossible from Israel for tourists) if you have an Israeli stamp or visa on your passport. Visit Syria before you go to Israel and after you visit Israel forget going to any other Arab country in the Middle East or Africa except Egypt and Jordan unless you have a paper visa and no stamps from the border or airports from Israel on your passport. Some people who hold dual citizenship and passports can avail of this advantage and show the other passport in Syria.

Direct passage from Syria to Israel via the Golan is not possible. There's however a possiblity via Jordan if you have two passports. Fly from Ben Gurion to Amman or drive via Allenby. Then change passport and drive to Syria. Don't display any items with Israeli origin.

only as a member of the UN. also, if you have dual citizenship, its possible to enter jordan at the alenby crossing, then drive about 50 miles north and cross the syrian border with your second passport.

It is not possible. Technically, Israel and Syria are at war. The whole border is military restricted. As well, an Israeli stamp on your passport = arab countries (with possible exception of Egypt + Jordan -?-) will refuse you a visa. Ask to have an Israeli visa on a SEPARATE paper. And NEVER display anything Israeli-related in Arab countries neibouring Israel. it would/could be perceived as provocation.

Go to Syria first, then to Israel. It is near impossible to do it the other way around unless you are will to wait until your current passport expires.

No, you can't. The Golan Border is not crossed, some relatives stand on both sides of the borders and shout in order to exhange their news.

There is a nice view from Um Qais (Jordan) on the heights and The Sea of Galilee. That might be interesting for you to see. There is always the option of keeping the Isreal visa and stamps on an external paper that can be handed on departure from Israel. This is a good option if you want to keep the flexibility of visiting Syria in the same trip and future.

When we went we could not cross the border.

You can go via Jordan, but there is no direct link. And remember, that after visiting Israel, going back to Syria is forbidden.