G.F.
We recently did my twins 3 year birthday party at Paradise Pond in Grapevine. It's fantastic. (It's off of main street housed inside of First Baptist Church of Grapevine). It is a fabulous Indoor Playground and they have free play on Thursdays and Fridays 9-11am. There is a large climbing structure with a slide, a bounce house, and several "stations/mini-rooms" with a variety of activities (e.g. one that is a mini-grocery store, one that has cars/trucks, one that has legos, one that is for dress up, etc). Be sure to bring socks for your kids to wear as they are required to play.
www.VineKids.com
301 E. Texas Street, Grapevine 76051, United States
I think you and your little one will enjoy it. I definitely give it a major stamp of approval as well in terms of renting it out for a private party (our twins bday party was wonderful)...they just book fast.
It is hard to find good indoor play spots. In terms of your requirement for finding something open on Mondays. I know it's not the best in the world, but our close-to home backup on a day when it's not good to be outdoors is the McDonalds playarea at the corner of Davis and 1709 in Keller. It has good climbing tunnels with a slide, and also a mini-slide on the exterior. We also have done the Chicfila on 1709 in Southlake but it is quite a bit smaller.
Best wishes!