She texted the other day and said "I really don't like that I won't get to see you this week," and suggesting a lunch date or something. This is my busy week with my daughter, my free time is practically non existent. Next week will be lighter for both of us, but still there are only certain days we'll have mutual free time. She's not pushy in a "show up on your doorstep" sense, I guess she's just coming on too strong in general. Last weekend she asked if we could spend Friday night and Saturday night and all day Saturday together. No. I have shit to do.
Aha! This clarifies your dynamic for me. She is...kind of annoying, yes? Or at least, you find her requests to see you more frequently annoying. (And I would certainly find her annoying if I were dating her).
Instead of understanding that you have no free time this week, she is pushing you to try to finagle your schedule to fit in a lunch date. Because she "doesn't like" that SHE won't get to see you.
This isn't a poly issue. It's a compatibility issue. She is someone who wants to see her partner(s) as often as possible, and you are someone who is more independent, values alone time more, and has more commitments on your time.
It may not even be that her feelings for you are stronger than yours for her--it may just be that her style of dating (for her partners who are not comet partners) is not compatible with yours.
You need someone who can understand that you aren't available some weeks and that you don't have full weekends free. She needs someone who is available to see her multiple times per week (or whatever).
The poly component is that you have no time to put effort into dating/meeting other people while she is demanding so much time from you. Meanwhile, she has time to see you plus a few other people. So, you are starting to feel resentful, and even to question being poly itself.
But, that's really a side issue. The main issue is the mismatch in how often you want to see each other.
I think you need to communicate this to her better. Actually sit down with her to talk about this mismatch. Whether it's about incompatible dating styles, or feelings that aren't as strong on your part yet. And then decide what you should do about the mismatch.
Sometimes people are incompatible regardless of polyamory or monogamy. Other times, there are things that would be dealbreaker incompatibilities in monogamy, but can work fine in a poly arrangement.
For example, Person A is looking for a primary partner who wants to see them 3 times a week and most weekends. Person B likes Person A, but isn't looking for a primary partner, isn't available that often, and doesn't want to see them that often.
If Person B is clear and honest about that, Person A can decide to either end the relationship and focus on finding the partner they want, OR they can decide that Person B would make a great twice-a-month partner and this would still allow Person A to have time to search for a primary partner.
But if Person B is ambivalent--not establishing clear boundaries on their time, agreeing to stress themselves out carving out more time for Person A, saying they think they'll have more free time in the future, etc--then everyone will end up miserable.
Or, if Person B is clear about what they want and don't want, and Person A agrees to the terms but secretly hopes to change Person B's mind...that's also a recipe for misery all around. (I'm not clear on how to prevent that scenario, though).
But, my point is, it starts with clear communication about a mismatch in expectations, wants, or feelings.
Mostly, I think at this stage I do want to devote a proper amount of time and focus to her. I don't want to create or foster unrealistic expectations (such is the dilemma, I suppose) but at the beginning of a relationship I think it's fair to give a little more, giving things a chance to develop, understanding you can settle into a more practical schedule after a little while.
I agree with IndieSolo that you may want to rethink this philosophy of giving more time early on. Because the other person won't understand that you are creating an impractical schedule for yourself, in the hope that the schedule will become more practical for you (i.e., will fit your life better) later on. Then you will find yourself dating someone whose life, time, and schedule don't match yours.
Maybe be clear that you like to maintain a lot of independence and time to yourself early on. That way, you can find someone who is actually compatible with what you're looking for.