If the premises which have been let are in England and Wales, read this thread:
http://www.consumeractiongroup.co.uk...-landlord.html
If the premises which have been let are in England and Wales, the rights of the parties are those which are set out in the written tenancy agreement.
The question of whether the tenant has the right to use the hot tub is one which can only be determined by examination of that written agreement. Consult a solicitor for advice.
The question of whether the landlord has a contractual right to enter the premises is also one which can only be determined from the actual terms and conditions in the tenancy agreement. Again, consult a solicitor.
As a matter of law, the landlord has given exclusive possession of the premises let by the tenancy agreement to the tenant. There is no implied right for the landlord to enter the premises which have been let.
You will want to consider carefully (a) the extent of the premises that are included in the letting, and (b) the express provisions as to access by the landlord to those premises - there can be NO implied right of access.
The statutory right of access to repair, under section 11 of the Housing Act 1988, does not apply in the situation as described by you.
If the tenancy agreement contains an express right of access by the landlord, you can only enter in accordance with the terms of the relevent provision in the agreement. That provision will set out (a) what period of notice must be given, e.g. 7 days or 21 days notice, and (b) in what form the notice must be given, e.g. by letter.
If the tenancy agreement is silent on the point, the ambiguity will normally be decided by the court in favour of the tenant.
It is important to have a professionally prepared letting agreement, which spells out in detail important points such as these.
There are various criminal offences which you might commit if you enter the premises without an invitation from the tenant, in breach of the provisions of the tenancy agreement.
Advice & opinions on this forum are offered informally, without any assumption of liability. Use your own judgment. Seek advice of a qualified and insured professional if you have any doubts.