Should I get a BritRail pass?

If you will both be traveling together on all train trips, consider the option of buying a two together railcard. The card costs 30 pounds but then gives 1/3 off most trips (Valid Off-Peak Monday to Friday and Anytime at weekends and bank holidays).
https://www.twotogether-railcard.co.uk/

Price out your routes using the two together rail card and then compare with brit rail pass. Which is less expensive? You can look these up on the National Rail website

Is the order of your trip fixed for some reason? It would make much more sense to visit Alton from Weybridge, as they are only 35 miles or so apart.

It depends if you want flexibility, or are happy to book on specific timed trains.

If you book reasonably far in advance you can get Bath to Windermere on a mid morning train (via Bristol and Birmingham) for as low as £28 each with railcard reduction, and Windermere to Alton for £38 each (including the tube fare across London). In this case I am looking 8 weeks ahead. These are Advance Fares for specific trains only.

For £37 each you could do Bath to Penrith then from Easter to October take the Penrith Railway Station to Bowness Pier direct bus every 2 hours over the Kirkstone Pass. A great introduction to Lake District scenery.

So it depends when your trip is.

If it is short notice and/or you want to just hop on any train then Britrail will pay.

I do like the flexibility of the BritRail England Flexipass, and if I’m reading it correctly, I researched and found that I can get a Standard Senior pass for around $330. 8 days in 1 month. I feel like I’d be more comfortable not having to meet strict deadlines and booking train trips in advance, so in that sense, it’d probably be worth it to me.
One of our party leaves us after our trip to Weybridge - ( spending the day and night here to visit childhood home) - fantastic deal and last room left on accommodations in Bowness so don’t want to change dates and mess that up!)

Then that's fine- $330/£270 for 8 days is £35 a day.

A flexible Bath to Windermere senior railcard is £116 and Windermere to Alton £112. So that's £228 + £13 London to Weybridge + £11 Alton to London + Weybridge to Bath £34= £286. Those 5 days have covered the cost, with 3 days yet to use.

Thank you for helping me to clarify!!