This situation requires a two-pronged approach.  The "conflict" is arising because you are all fed up with this person who is taking time off sick.  You don't actually know WHY she is taking time off sick and you are not really entitled to that information - only her manager is.  But you still have to pick up the work.

Firstly, there is the work to be done.  Ideally, the burden of work would be shared in half or whole days amongst the pool of admins.  You don't say much about your reception/company set up, but if reception has a computer which is linked to your company network, then it may be possible for the person at reception to continue doing some of their own work.  

Secondly, someone - perhaps the senior admin if that is you or someone else - should speak to their manager about this matter.  The fact that you are fed up with your receptionist colleague is not the issue here; the thing you need to emphasize is the impact it has on your ability to do your proper jobs.  If you can provide evidence - such as projects being delayed etc - then maybe something concrete could be done.

The matter of sick leave should be addressed by a good manager.  It is possible that your receptionist is swinging the lead and taking sick leave when she just doesn't feel like going into work.  It is also possible that she has a chronic condition which means that she cannot always guarantee she will be fit for work.    There are a number of conditions which come into that category and which cannot always be managed by medication.  I had an assistant some time ago who had two serious conditions which meant that she took more days off sick than one might expect, but her conditions were statemented to us by her doctor and so we made allowances for her.