So first, get out of the way the obvious, there's no law saying you have to marry this gal today or any day, can even live together happily ever after without getting Jonny Law involved. If you already have had your children, then really there's nothing wrong with being in love and enjoying rest of your lives. In fact, without the false chain of potential divorce, is so much easier to experience real love and even battle through future problems. Is hard when you are trapped, like many men here are, in marriage no one wants to be in, but divorce is worse, with children and money and property involved. My dad has been married four times, and really even he now agrees with the above advice, which I and my sister gave him in 1996 after his second marriage. No need to make something that could be awesome messy.
Second thing, this may be harder to do because it takes some deep thought and maybe time, but consider thought exercise. Why did you get married first time? What parts of THAT decision ended up spoiling the time that you got divorced? Like you and your ex wife made some mistake then which later grew into reasons to no be married. Sometimes it might be people get married "because", or they get pregnant, or you both liked fucking each other, all reasons which become null after some time period.
Either way, enjoy the ride. One of the joys of my life is meeting an unhappily married lady and hearing those magic words, "my husband doesn't fuck me anymore". Ladies in their late 30s, 40s, 50s who are divorced either in practice or in law, wow if you got the power they are an endless fountain of sex energy and also love. They know, just like you might know now, life is no long, and there is time when you may wish you had someone special. For ladies in this situation, they may be over hungry and this is why you got the L word thing. Or, they are so used to tossing that word around, from being married for years or decades, that it really is unintentional.
Go easy, enjoy yourself, and keep in your mind that you're a free man, don't be in any hurry to get locked down. I see a lot of unmarried but long-term couples at the club in the last ten years, it's becoming somewhat common now.