Mother of my boyfriends children wants to meet

A little background info: I've been dating this man for a year and a half. I met his daughters about 6 months ago. They come to our house most fridays for the evening and we hang around, watch netflix, play games and eat takeout. They are 8 and 13. Super sweet, polite, well behaved girls. I really enjoy spending time with them. I actually never wanted kids until I started dating this guy so I don't know anything about kids in general which makes me really nervous. None of my friends have kids except one who has a 2 month old so I often feel like a fish out of water when im with them but I really want to be the best I can be when taking care of them. I'm 32 and he's 33.

Anyway, my boyfriend told me yesterday that their mom wants to meet me before they can start spending the night with us. I'm pretty cool with this because I know I wouldn't want to send my kid to a strangers house. I also think she's done an amazing job raising them so I admire her for that.

I'm just curious to hear if any of you ladies have has this experience and can share some stories or tips on what to say or something. Is this a common thing?

We haven't made any plans so I have no idea when this will happen but I know when it comes I will have a lot of anxiety about it so I thought if I got some insight from the Glow community it would help ease my fears a bit. I guess I'm just a little bit worried because what if she's asking for this meeting with some ulterior motive like she wants to size me up as competition or something as I do get the impression that she would get back together with him if he wanted to get back with her though I don't believe he does.

Thanks for your help!