I've been inside all three.
You need to pre book the interior Parliament tour. It's an hour tour though I'd set aside 2.
Westminster Abbey can easily take an hour or longer depending your interest and whether you use the audio tour and walk around on your own or take a guided Verger's tour. I'd plan 3 hours.
Churchill War Rooms can be done in an hour.
So yes it is possible but given your mother is 72 and your husband has mobility issues you'll need to factor in those realities and decide if it's a pace that works for you.
At Home In London which I believe I've suggested before or Home Away are other websites to review.
You might also check out the apartments that Vancouver Studio Apatrments operate.
I'll be in the UK in November for business and pleasure. Already confirmed accommodation and airfare.
2 years ago booked 3 Parliament tour tickets in May for November visit. Sadly the day before my friends departed from the states one took a horrific fall down the back stairs of their home.
INstead of returning the tickets I wandered by Parliament one morning in order to give 2 of the tickets away.
Took all of 10 minutes to find an older couple who had an interest. They insisted on paying and I said,
" how about buying me lunch instead? ". Walked over to the 3 Chairman pub and enjoyed a lovely few hours of conversation and dining.
Saw them again the day of the tour. We've kept in touch.
Nearly book all tickets in advance. Everything but theatre. Perfectly pleased to use the half price TKTS at Leicester Square for my theatre visits.
Purchasing in advance is up to you. I do it so I'm not disappointed. Matter of convenience. My mode of travel.