It sounds like what you're experiencing is "bridging." There's a "bridge" of tissue at the base of the opening of the vagina. When stretched, it will occasionally separate or tear. As we lose estrogen through menopause, those tissues lose elasticity; there's also narrowing of the opening of the vagina.
A very successful solution is a "perineoplasty," a surgical modification of that tissue. Like a small episiotomy (sometimes done in labor to ease childbirth), it involves a small incision and repair to relieve pressure. In this case, the repair is made from front to back rather than from side to side.
This procedure is done in the office, under a local anesthetic, with just a few absorbing stitches. In my experience, it's very successful and much appreciated by women. Keeping things comfortable will often require some combination of localized estrogen, vaginal moisturizer, and a lubricant with intercourse.