The Downside of Dating Single Parents

I'm a single mom of a teen daughter. I'm really enjoying this time with her - our communication is admirable, we honor one another's personal space, and set boundaries, respectively.
I like who I am!
I love how far I've come; lots of growth and self-awareness due to the support of recovery. I'm hesitant to date anyone with small children (to be more specific, under 18 yrs) including men with grandchildren.
As a woman turning 50, I've gone through the stages of infancy to middle school and all the emotions in between. I've dated single dads - divorced, widowed, etc. - whose profiles were accentuated with the common phrase 'their children come first' and found they weren't fully present.
Friends have suggested that I be open-minded (one persistently asked if I would date her ex-husband. They co-parent two boys - 9 and 7. I gave a hard 'no', twice, after hearing their history together). Look, I feel complete in this area. How do I lovingly care for myself in profiles while turning down possible offers from SSD (single straight dads)?
Well, the first thing to understand is that - regardless of the child's age - the man's children will - and should! - always come first. To date a man that doesn't put his kids first would mean dating a man who is a bad parent.
I'm going to disagree with your friends and tell you not to compromise on this. My reasoning is due to personal experience. My Dad was a widower with five daughters ranging from ages seven (me) to nineteen. A year after my Mom died, he met a woman who had three boys of her own. My Dad frequently took me out on dates with this woman because he couldn't find a baby-sitter. You can imagine how thrilled she must have been at that. They got married a year later. I loved my step-mother. She was not my mother, but I considered her a parent and a friend. All of my sisters did. After my father died, my step-mother told me, "Christan, never date a man with kids." It seemed like an odd thing to say given I was her step-daughter, but I chalked it up to grief. At this point in time, just a few weeks after my father had died, all my father's money (save for some small trusts he'd set up for my sisters and I) and properties and cars and whatnot defaulted to my step-mother, as we hadn't found my father's will. Her name, along with his, was on everything.
About two months later, my step-mother was diagnosed with Stage 4 lung cancer. Nothing could be done. She had maybe a month left. At my step-mother's request, my sister quit her job as a home health aide to care for my step-mother. My other sisters were there every day, for whatever she needed, along with our step-brothers. Little by little, though, we were discouraged from being at the home she now owned. They said they just wanted it to be them and their Mom. Understandable, give she was in her final days.
A few days after she died, my sisters and I learned my step-mother had cut us out of her will and left may father's sizeable estate to her sons. That comment she made about not dating men with children still haunts me to this day. How she must have resented us all those years for her to do what she did. It shattered me in ways from which I have still not recovered.
If you don't want to date men with kids, don't. You'll resent them and, eventually, him.
Now, as to how you can meet the type of men you want to meet, let's start with your profile. First, there's no need to put any kind of disclaimer in your profile of who you don't want to meet. Instead, you should focus on describing yourself and your current lifestyle. Include the age of your daughter and share that you're enjoying the freedom that comes with a daughter of seventeen (or whatever her age may be.) That will give men reading a heads up that you're probably past the stage where you want to deal with relationships that involve younger children. If you're very physically active, include that, too. You want to paint a picture of your current lifestyle so you can attract someone with a similar one.
Let people read your profile and decide for themselves if they feel they're an appropriate fit. Disclaimers do nothing but give the impression you've been burned, are jaded or otherwise vulnerable. The make you the perfect mark for the wrong people.
As for not wanting to date men with grandchildren, I would like to encourage you to be honest with yourself if the true issue is you don't want to date men your age or older. If that's the case, that's fine, but better to be honest with yourself so you can be clear with your intentions and attract the right people. The age issue is a common one shared by men and women equally. In my line of work, I've encountered many women and men who aren't quite ready to accept they're no longer in demand for singles in a certain age bracket. They think they're too vibrant or can pass for younger, not realizing that neither matter to the objects of their affection. Not for long, anyway.
Also be honest about wanting to be the main focus or priority of a man's life. I've dated single Dads and, like you said, the were never very present. But then, I was never 100% present either, as I was always worrying about something else - something very important to me - like my coaching certification course, this business, money, etc.
I'm not sure it's possible for anyone to be "fully present" in a relationship, especially if they've been single for a long period of time. I actually think it's a good thing that we stay our first priority (after our children, if we have them) and not lose ourselves in our relationships. Maintaining our identity and independence throughout a relationship because, let's face it, that other person will not always be there. Look at what's going on now with COVID-19, especially in regards to dating. My love life has consisted of Skype drinks and Zoom shared-screen movie nights. Not only am I grateful to have my health and to be able-bodied at this time to be able to work, I'm grateful that I enjoy my own company and can be alone with my own thoughts. That comes from knowing how to be single and being comfortable alone.
As I said earlier, while I suggest you be a bit flexible on the ages of these men, if you don't want to date men with young kids or children still heavily dependent on their Dad, don't. There are few things that I advise to hold your ground when looking for a partner, and that's one of them.
Good luck!