You’re 24. You get to decide who to date, live with and marry without your parents’ approval.
That said, it’s understandable to want your parents’ approval — on some level we all do, and it’s much nicer to be with someone your family and friends like, than someone they don’t. However, your situation requires more maturity than you’ve probably had to exercise before. To do this, understand their feelings. They probably have antiquated views of single mothers. Even today many people still see single mothers as tainted and not as good as someone who is more “virginal”. The same goes for divorced women without children. Instead of judging, just understand it.
If your family is open minded, you can quote them all sorts of facts from the United States Census Bureau and other statistic gathering companies about how almost half of all marriages involve a spouse who was previously married, etc. A staggering number of marriages end in divorce and these divorced people are part of the ever growing dating pool, so your finding someone who happens to be divorced is pretty much the norm. That said, single parent relationships and marriages are different than those without kids involved, and your parents may not know a lot of people who’s adult children are dating or marrying single parents, so this may feel like a freak show to them. If, over time, they can’t wrap their heads (and their civility) around this, then you need to give them space and make your commitment veer towards your girlfriend.
It’s hard to change people, so my advice is be understanding of your parents, but clear on your own intentions and behavior. You’re not a child, and I trust you have your own home and job, so dealing with your parents’ feelings is not as important as your own character and life.
I hope this helps.