I'm an American who has lived in the UK, Dallas, and the Bay area of California. I'd say definitely go for it! Your kids are at an age where the transition should be easy, and being a part of a school community will give you a place to make friends quickly.
Dallas would be a good choice if you are interested in exploring the whole of the US -- DFW airport puts you in a perfect position for direct flights to either coast and places in between. And Dallas has many direct flights back to the UK. California would be a good choice if you love nature and are excited about West Coast adventures with your family. I know you said finances are not a concern but cost of living is so much higher in California than Texas, so you'll want to do your research to know what to expect.
I can relate to your worrying about your mom. My mom is a widow and I hated being so far from her. But she found travel between Dallas and London really easy, and we had a lot of memorable and fun visits. If your mom will let you fly her over, she may really enjoy visiting you in the US. If the situation changes, you can always reassess and move back closer to her.
We ended up moving to Dallas when my DS was preschool age. It's a sophisticated and nice city, with fantastic shopping and restaurants. The summers are very hot but you just need to have a pool or access to one! I did not mind London weather at all, but I did realize once back in Dallas that the frequent sunshine had a great effect on my mood. If you do choose Dallas, I would suggest you go for one of the North Dallas private schools, rather than the public schools in the Park Cities or Plano. I just think that the culture at some of the private schools would make an easier transition coming from the UK. Feel free to PM me about schools.
I don't know much about life in Silicon Valley, but we moved to the East Bay not long ago and really like it. It's friendly, beautiful, expensive (home similar to our Dallas one would be at least 3 times as expensive here), politically liberal, which we like. We have natural beauty right where we live, and many beautiful places a short drive away. However, we are finding it limiting being such a long flight from the East Coast of the US and from places we want to go in Europe. A lot of people seem to vacation in Lake Tahoe and Hawaii.
Sorry that was very long! Good luck with your decision.