Finally found a moment to give an update...
In the absence of being able to pin down Pleasant Terrace, it's occurred to me that there might be records at Salisbury Hospital, where Clarissa's second child died, which might yield more information. I believe these are at the Wiltshire and Swindon History Centre, but if anyone has any experience of these, I would be interested to know.
After some painstaking cross-referencing of various census years, and mapping addresses, I have had more luck with the address in Bournemouth:
2 St Michael's Round later became 3 Purbeck Road, when the whole street was re-numbered.
Western Gazette, 2 March 1897
Advert
Girl (strong) wanted, age about 16 - Apply Mrs Grant, 2 St. Michael's Round, Purbeck Road, Bournemouth
The family in 1901
RG13 Piece 1040 Folio 89 Page 37
Great find, thank you for this! It seems Mr & Mrs Grant lived at this property for a good number of years, and would've been present during the period when Clarissa stayed there. I was amused by her specifying a strong girl, but perhaps it's because he was a baker.
I note that Mr Grant is the only person on the electoral register for this address over the years. Perhaps they rented out rooms, or perhaps it was the responsibility of a landlord. Certainly, Clarissa must've been happy to return here for the second birth.
My late mother-in-law’s mother was living in a home for fallen women when MIL was born, although the birth did not take place there. I wondered if yours was a similar situation with the address in St. Michael's Rd being one of the numerous homes in Bournemouth, but I cannot find anything to indicate it was.
Thank you, Jebber. I've been spending some time considering what you had to say. There is nothing to indicate that it was a specific place for expectant women, judging by the other tenants in the property in 1891 and 1901. However, I can't imagine many boarding houses would take in women in her situation, and I wonder if there was a covert way this was advertised. Clarissa must've stayed here some weeks, as neither of the births were registered until about a month afterwards. I wonder if she had a monthly nurse staying with her - after all, I can't see how she could've afforded her lifestyle by herself, especially if she had her young son in tow too, and to have been by herself in a strange town, albeit away from prying eyes, would've been a tough ask.
I can better understand her journeys to Bournemouth. The area at that time seems filled with incomers, and it would be easier to tell whatsoever story, and no-one to be any the wiser.
However, I am still mystified as to her extended sojourn in Salisbury. I have found no connections in her family to Salisbury (or indeed Bournemouth, or Yeovil), and she had plenty of family back in London. Hence why I have imagined it was at the bidding of Mr X. I wonder if anyone knows if there were particular reasons drawing people to Salisbury during this period?
Thanks again to everyone for all your kind help with this