Without written records or reliable eyewitness testimony would have to use an increment borer to be sure.

I'm so sorry you lost your tree, believe me I know how you feel, it happened to us, I was heartbroken as well....:-( Believe me I'm no expert, I just posted a question about Norwegian Spruces, but I'd hate to see you cut down a healthy pine tree to even up your tree line. Are there any garden nurseries around you that can locate a large pine tree and transplant it for you. Here in upstate NY, we have several tree farms that are willing to dig up a nice size tree. Your talking tractors, back hoes the works. We picked out a large birch from a tree farm when we first built our house.... they dug it up, shipped it over on a flat bed and transplanted it for us. Would you believe they gave us a years guarantee. It was a little pricey, but well worth it. It stands proud in our courtyard today. Pretty sure someone here will suggest a tree that would blend in nicely so you won't have to cut down the other tree. Your tree lined driveway is beautiful. Let us know what you decide..send a picture. Good Luck!!!

Oak can be considered a weed species, if unwanted trees grow in your garden. And yes prolific seeding Ash can be definition of weed species. But know Ash does this, because its a "Pioneering" species. And also an ecosystems most influential Keystone species keeping, other invasive species in check. While securing ground so pre-settlement species like Oak can come back someday! Ash Pre 1950 before popular cultivars like Marshal seedless were sold by nurseries, Green Ash was even more iconic than Sycamore for its production of one strong apical dominant leader. These "Plant and grow above your roof" Green Ash can still be found today with ages of 60 and older. In fact, its a good way of estimating a trees age, and can determine if ones ash is younger or older than 60. So presently all the Green ash with one Roman column sized trunks, are those pre 1950 grown examples. A few owners who lost their old wild ash trees to EAB, but are keeping a seedling or two growing. Are shocked how their young trees require no structural pruning because they continue to be so apical dominant. One big difference between Green and White Ash, is how growth on end of limbs on Green Ash, curve upward. And growth habit of White Ash results in all limbs and branches pointing straight upward. White Ash, Sugar Maple, and American Elm, are powerhouse species that can handle growth of multiple limbs extending outward from one lower spot on trunk. Compared to say Callery pear trees, which fall apart with this growth habit. Those three hardwoods with this common trait, can continue to have conglomerate of multiple leaders stay well attached without self destructing. Horticulturally this is because they can handle included bark attachments, actually strengthening overtime by developing into one whole common mass of wood. As a Dendrologist observing thousands of felled trees, one cannot tell from outside that many times one single trunk had been made up from two or more trunks on Green Ash. And when compared to other species that produce twin trunks beginning low to ground, such as Silver Maple. Green Ash can easily become multitrunked tree, producing strongest attachments without fatal problem of included bark. For example, look at a Silver maple diverging into two large trunks, from a sideways view. And you will see pinching bulge extending outward. Yet on Ash with same structure, there is no pinch bulge. Because where two trunks converge, is all same wood without included bark in middle. Know that even Oaks can develop multiple leaders, when grown out in open. And when one finds an older multileader tree growing in middle of forest with all younger single leader trees surrounding it. These examples are called "Wolf" trees, which began growing after settlers cleared local forest during 1800's. Then new forest was later allowed to reclaim old riparian farmland, usually around 1900's. Its great that you all notice different unique growth habits between Green and White Ash. Even cooler is fact that there can be huge differences between wild species evolving from unique local conditions. So traits I point out, may not be true for Ash growing in your local area. One great example, is the wild variety of Biltmore White Ash from Ashville North Carolina which FL Olmsted had discovered. Which has pubescent fuzz on back of leaves, like Red Ash. At same time Scientists consider Red ash, just a variety of Green Ash. Another example is Junginger Autumn Purple White Ash variety a scientist found in Wisconsin local woods. And all those urban ones you see today, are clones that cannot seed. And before clearing of American forest which extended unbroken from East coast to Mississippi river. Tree hunters regularly discovered unique one of a kind examples they would officially characterize and list traits of. Then propagate new trees from cuttings for planting elsewhere.

We really do need to see photos to determine what is going on, otherwise we are just guessing and you then may be following advice that is not appropriate or could even prove harmful. FWIW, horticultural oil is NOT a suggested treatment for borers.......if that is what you have. Because the larvae tunnels (bores) into the wood of the tree, any sort of topical approach has to be carefully considered and timed to have any effect. The bugs are not inside the bark....they are inside the tree and it often requires a systemic (seldom recommended for edibles) to ensure effective control. And the appearance of sap - aka gummosis - can arise from a multitude of conditions, not all of them serious or requiring treatment. Photos, please!!