The fact that you aren't jumping at this is telling me that your spidey senses are tingling and you need to listen to them.
She likes you (what's not to like??) and she wants to be your friend which is nice but she's coming on too strong and it's making you feel uncomfortable (am I right?). That's ok. She might end up being a good friend down the line and it's easy to get too much in a person's space when you meet someone you feel like you really like and have a special connection to.
She's left it up to you about dinner. let it hang--you've already told her you are crazy busy. If she invites you again, tell her honestly that it stresses you and DH out having the boys over at someone's house for dinner because of their picky eating and active dinnertime behaviour.
giving her the benefit of the doubt, I think she's excited to meet a like-minded person and got ahead of herself. Let her cool down and see how it goes. I think it's fine to be vague and not say no outright and ok to not give a date. If she keeps insisting, tell her that life is just nuts right now and that perhaps you and her can have coffee together in early March when you feel you might have some breathing room. Tell her that surely she remembers how hectic it can be with young kids and their school activities and how even the thought of an extra outing--although a fun one-- would be hard to find a mutually convenient time.
She might be one of these up/down people. If you found her too "enthusiastic" it could be that and she'll back off in a bit. But it is tricky because (I feel) you don't want to hurt her feelings or insult her. and because of that, I'd say, yeah, I'll call you (making that phone sign with your hand) lol
good luck and I'm glad you invited that other stranger into your home. You are a big sweetheart!
me:42, DH 44
DS: born by c-sec Apr15'03, 9lbs5oz 41wks gest. (after 4 years of ttc, starting in 1998)
DD born by c-sec Oct 13 2007, 8lbs13oz 39wk gest. (after just under 3 years of ttc)
~~DS was conceived naturally the cycle following a cancelled DE IVF, using my good friend's eggs. She was on the verge of hyperstimming.
~~DD's nat conception I attribute to using OPKs like a crazy nut, eating grapefruit daily and using preseed. also 5 cycles of TCM ending 2 cycles before that lucky cycle.