This is almost the exact situation I was in.
We had a mortgage, a DC, to be fair I did have a ring, but DH keep putting off the actual wedding. A load of excuses, money, family making it difficult (both our sets of parents are divorced and remarried and it would have been a nightmare having them all in the same room)
When we started talking about baby number 2, I gave him an ultimatum and basically said I wouldn't until we are married.
So we did. Registry office in secret, just us, DS and 2 witnesses, followed by pub lunch. Everything, including my dress (I did manage to wear an actual wedding dress, although it was a short one) came in at less than £500. And no bother with family.
We told them after we came back from honeymoon (which was actually a holiday booked long before we even decided to book the wedding, and planned the wedding date around it)
Just do it. It's also an exciting and fun story to tell the grandkids, and if your DP likes dining things differently from other people then I may appeal to him.